Showing papers on "Prime (order theory) published in 1980"
TL;DR: In this article, two experiments were conducted in which subjects labeled target pictures preceded by either semantically related or unrelated prime pictures, and exposure duration of each prime was varied around a threshold value, established separately for each subject, that represented the minimum viewing time necessary to identify the prime picture with 100% accuracy.
Abstract: Two experiments were conducted in which subjects labeled target pictures preceded by either semantically related or unrelated prime pictures. The exposure duration of each prime was varied around a threshold value, established separately for each subject, that represented the minimum viewing time necessary to identify the prime picture with 100% accuracy. The results of the first study indicated that semantic-priming effects can be obtained with pictures at prime exposure durations too brief for conscious identification of the prime to occur. Data from the second experiment provided an estimate of the minimum exposure time necessary for priming under these conditions. There was evidence from both experiments that attaching a name to a picture is an attended operation that can interfere with naming a subsequent picture, independent of any semantic priming that might occur. This indicates that extracting the meaning from a picture and consciously identifying it may be separate processes. The results are discussed in terms of current models of picture perception. Language: en
177 citations
TL;DR: In this paper, it was shown that the partners in an extension of commutative rings R ⊂ T have the same prime ideals, i.e., in which Spec(R) = Spec(T) is a pseudo-valuation domain and T is a suitable valuation overring.
Abstract: There are numerous instances in which the partners in an extension of commutative rings R ⊂ T have the same prime ideals, i.e., in which Spec(R) = Spec(T). Although this equality is intended to be taken set-theoretically, the identification easily extends to the corresponding spaces endowed with their Zariski topologies (see Proposition 3.5(a)), but of course need not extend to an identification of Spec(R) and Spec(T) as affine schemes. Perhaps the most striking recent illustration of this phenomenon arises from the work of Hedstrom and Houston [14] in which R is a pseudo-valuation domain and T is a suitable valuation overring. Other examples may be found by means of the D + M construction, either in its traditional form [12, p. 560] or in the generalized situation introduced by Brewer and Rutter [5].
160 citations
Patent•
15 Dec 1980
TL;DR: A public-key data encryption system employing RSA public key data encryption including a message encrypter capable of encrypting messages using a non-secret encryption key, and an encryption-decryption key generator, including a microprocessor or other large-scale integrated circuit or circuits formed to generate a sequence of prime numbers as discussed by the authors.
Abstract: A public-key data encryption system employing RSA public-key data encryption including a message encrypter capable of encrypting messages using a non-secret encryption key, a transmitter-receiver coupled to the message encrypter which transmits or receives an encrypted message to or from a remote location, the transmitter-receiver also being coupled to a decrypter capable of decrypting a received encrypted message using a decryption key which is a secret input to the decrypter, and an encryption-decryption key generator, including a microprocessor or other large-scale integrated circuit or circuits formed to generate a sequence of prime numbers beginning with a selected known prime number having a length relatively short with respect to the desired length of the last in the sequence of prime numbers, and which is constructed to form the sequence of prime numbers in the form hP+1 where P is the preceding prime number in the sequence, and to test hP+1 for primality by first determining if hP+1 has a GCD of 1 with x, wherein x is a composite number consisting of the product of all known prime numbers less than or equal to a pre-selected known prime number and if the GCD is not equal to 1, incrementing h to form a new hP+1 to be tested for a GCD equal to 1, and when a GCD is found to be 1, performing the primality tests to determine whether 2 hP ≡1 [mod (hP+1)] and 2 h ≢1 [mod (hP+1)], and if either 2 hP ≢1 [mod (hP+1)] or 2 h ≡1 [mod (hP+1)] further incrementing h and so on until a prime is found in this manner and then determining if the length of the prime number is of or greater than the desired length. If the hP+1 which has been determined to be prime is not of the desired length, hP+1 is placed in the sequence of prime numbers and a new h selected to be used to find the next prime number in the sequence in accordance with the above described procedure by forming a new hP+1 in which P is the previously determined prime number in the sequence of prime numbers. When a prime number in the sequence of prime numbers is found which is of the desired length it is input into the encryption-decryption key generator for generating the RSA public-key encryption and decryption keys.
124 citations
Book•
31 Jan 1980
TL;DR: In this paper, the authors introduce partially ordered rings and partially ordered fields for semi-algebraic sets, and show that they can be used to define semantically meaningful sets.
Abstract: Introduction 1. Partially Ordered Rings 2. Homomorphisms and Convex Ideals 3. Localization 4. Some Categorical Notions 5. The Prime Convex Ideal Spectrum 6. Polynomials 7. Ordered Fields 8. Affine Semi-Algebraic Sets
82 citations
62 citations
27 Jun 1980
50 citations
01 Apr 1980
TL;DR: In this paper, it was shown that A * = A *(I) is constant for any ideal I in a Noetherian ring, where I is a prime ideal of R and I is an integral closure of I.
Abstract: Let I be an ideal in a Noetherian domain R, and let I be the integral closure of I. Let A*(I) = Ass(R/Il) for n large (it being known that for large n this set does not vary with n). Suppose that R satisfies the altitude formula. Then it is shown that P E A*(I) if and only if height P = I(Ip), the analytic spread of Ip. Introduction. Let I be an ideal in a Noetherian ring. For n > 1, let A(n) be the set of prime divisors of I", A(n) = Ass(R/In). A recent paper of Brodmann [1] shows that A(n) is constant for n large. In [5] that constant is denoted A * = A *(I). In general it is difficult to explicitly determine A * for a given ideal I, although in [5, Corollary 22] this is done for R a 2-dimensional normal domain. This paper will discuss a concept related to A *, namely A *. Let I denote the integral closure of the ideal I, and let A(n) = Ass(R/I'), the prime divisors of In. If height I > 1, [5, Proposition 7] shows that A(n) is constant for large n. That constant is denoted by A* = A*(I). The purpose of this paper is to characterize A* for any ideal I in a Noetherian domain satisfying the altitude formula. The characterization is P E A* if and only if height P = l(IRp), the analytic spread of IRp. Preliminaries. Throughout this paper, R will denote a Noetherian domain, I an ideal of R, and P a prime ideal of R containing I. The domain T will always be T = R[Ix] = R + Ix + I2x2 + . . ., x an indeterminate. Since T c R[x], obviously the transcendence degree of T over R is 1. We will occasionally mention the form ring of I, R/I + I/I2 + .... Note that this is isomorphic to T/IT. If (R, P) is local, we will also use the ring R/P + I/Pl + I2/PP2 + ..., which is isomorphic to T/PT. Finally, P" will be P + Ix + I2x2 + . . . in T. If (R, P) is a local domain and I is an ideal of R, then l(I) denotes the analytic spread of I. Recall that there are various characterizations of l(I). (i) If R/P is infinite and if J is a minimal reduction of I then l(I) = v(J), the minimal number of generators of J. (ii) 1(I) = height(P"/PT). (See [7] and [8] for basics on reductions and l(I).) Also by the altitude inequality (stated below) height P + TRD(T/R) > height P" + TRD(P"/P) giving height P + 1 > height P" > height(P"/PT) = I(I). Thus height P > I(I). (See [2] for more.) Received by the editors July 10, 1979. AMS (MOS) subject classifications (1970). Primary 13E05; Secondary 13A15.
47 citations
47 citations
TL;DR: In this article, it was shown that if the number of agents n is a prime integer strictly greater than p, then there exists at least one efficient, anonymous and neutral social choice function, in short eanscf, that can be implemented by a dominance-solvable voting scheme.
42 citations
TL;DR: In this paper, it was shown that if n = 1, then such circulants always exist, and if n > 1, the circulant never occurs as the determinant of an integral $n \times n-circulant.
Abstract: The problem considered is to characterize those integers $m$ such that $m = \mathrm{det}(C)$, $C$ an integral $n \times n$ circulant. It is shown that if $(m,n) = 1$ then such circulants always exist, and if $(m,n)> 1$ and $p$ is a prime dividing $(m,n)$ such that $p^{t}||n$, then $p^{t+1}|m$. This implies for example, that $n$ never occurs as the determinant of an integral $n \times n$ circulant, if $n > 1$.
TL;DR: In 1736, Bayes wrote a tract on Newton's fluxions as mentioned in this paper, which was one of several explanations of fluxions which appeared following Berkeley's attack upon Newton's ideas in The Analyst.
TL;DR: In this paper, the intersection of maximal left ideals has been studied for the following classes of rings: (1) left V-rings; (2) left f-V-Rings; (3) left p-V Rings; and (4) left ELT R-rings.
TL;DR: In this article, it was shown that if an order q of an automorphism of an algebraic curve of genus g ≥ 2 is prime, then q≤2g+1.
Abstract: If an order q of an automorphism of an algebraic curve of genus g≥2 is prime, then q≤2g+1. In this paper we determine all curves having an automorphism of order 2g+1 when 2g+1 is prime.
TL;DR: The structure of the prime ideals and the prime z-ideals of C(X) has been the subject of much investigation (see e-g- [1], [3], [5]).
Abstract: Let C(X) be the ring of continuous real-valued functions on a (completely regular) topological space X. The structure of the prime ideals and the prime z-ideals of C(X) has been the subject of much investigation (see e-g- [1], [3], [5]). One of the surprising facts about C(X) is that the sum of two prime ideals is again prime.
TL;DR: In this paper, it was shown that no integral circulant of order pk exists with determinant pk+1, and that m is the determinant of an integral 9×9 circularant if and only if (m, 3)=l, or m = 0 mod 27.
Abstract: Let p be a prime > 3. It is shown that no integral circulant of order pk exists with determinant pk+1 . It is also shown that m is the determinant of an integral 9×9 circulant if and only if (m, 3)=l, or m = 0 mod 27. The proof makes use of a criterion which must be satisfied by the difference of two units in the cyclotomic field of level pk .
TL;DR: In this paper, it was shown that the commutator subgroup of a PN-group is p-nilpotent for each odd prime p. This paper is a sequel to [9] and our object here is to prove the following statement.
TL;DR: In this paper, a simpler, alternate approach to the prime ideals in crossed products of finite groups was proposed. But this approach requires the use of the induced ideal mapG instead of theν map.
Abstract: In this note, we offer a simpler, alternate approach to the work of Section 3 of “Prime ideals in crossed products of finite groups.” Indeed, by using the induced ideal mapG instead of theν map, we have eliminated many of the unpleasant computations of the original argument.
TL;DR: In this article, it was shown that the complete graph K n can be decomposed into edge disjoint cycles of the same length 2 p e if and only if n is odd, n ⩾2 p e and 2p e divides (n 2 ) where p is any prime and e is a positive integer.
Abstract: It is shown that the complete graph K n can be decomposed into edge-disjoint cycles of the same length 2 p e if and only if n is odd, n ⩾2 p e and 2 p e divides ( n 2 ) where p is any prime and e is a positive integer.
TL;DR: Theorem 3.3 and 4.2 in this paper are incorrect and must be replaced by the following condition: (1) П is a cyclic group, (ii) a dihedral group of order 2m, m odd, (iii) a direct product of cyclic groups of order qf, q an odd prime, f ≧ 1, where each prime divisor of m is a primitive qf-1(q 1)-th root of unity modulo qf.
Abstract: There are some errors in Theorems 3.3 and 4.2 in [2]. In this note we would like to correct them. 1) In Theorem 3.3 (and [IV]), the condition (1) must be replaced by the following one; (1) П is (i) a cyclic group, (ii) a dihedral group of order 2m, m odd, (iii) a direct product of a cyclic group of order qf, q an odd prime, f ≧ 1, and a dihedral group of order 2m, m odd, where each prime divisor of m is a primitive qf-1(q — 1)-th root of unity modulo qf, or (iv) a generalized quaternion group of order 4m, m odd, where each prime divisor of m is congruent to 3 modulo 4.
Patent•
25 Aug 1980TL;DR: In this article, a foaming agent is added to a conventional aqueous latex based prime coating and the coating aerated to give a frothed prime coating having a consistency of 500 to 750 grams per liter.
Abstract: In a method for prime coating fiberboard products the improvement wherein a foaming agent is added to a conventional aqueous latex based prime coating and the coating aerated to give a frothed prime coating having a consistency of 500 to 750 grams per liter, the frothed coating applied to the board product at a rate of 220 to 320 grams per square meter, and heated to collapse the froth and dry the coating
TL;DR: In this article, the authors present sufficient conditions on the ring R that all finitely generated reflexive modules give rise to prime Bourbaki ideals, which are analytically irreducible under certain conditions.