Showing papers on "Idempotence published in 1997"
Book•
30 Apr 1997
TL;DR: In this article, a generalized solution of Bellman's Differential Equation and multiplicative additive asymptotics is presented, which is based on the Maslov Optimziation Theory.
Abstract: Preface. 1. Idempotent Analysis. 2. Analysis of Operators on Idempotent Semimodules. 3. Generalized Solutions of Bellman's Differential Equation. 4. Quantization of the Bellman Equation and Multiplicative Asymptotics. References. Appendix: (P. Del Moral) Maslov Optimziation Theory. Optimality versus Randomness. Index.
425 citations
TL;DR: In this article, a class of simple Lie superalgebras induced by Novikov-Poisson algesias are introduced. Butler and Srinivasan constructed a class without idempotent elements.
106 citations
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TL;DR: In this article, the general form of continuous, symmetric, increasing, idempotent solutions of the bisymmetry equation is established and the family of sequences of functions which are continuous and symmetric and increasing, and decomposable is described.
Abstract: The general form of continuous, symmetric, increasing, idempotent solutions of the bisymmetry equation is established and the family of sequences of functions which are continuous, symmetric, increasing, idempotent, decomposable is described.
34 citations
TL;DR: It is obtained that the problem of determining if a finite poset admits a near unanimity function is decidable.
23 citations
TL;DR: This work reformulates denotational semantics for nondeterminism, taking a nondeterministic operation V on programs, and sequential composition, as primitive, which gives rise to binary trees.
16 citations
TL;DR: In this paper, the structure of nonnegative matrices dominated by a nonnegative idempotent matrix under the minus order is described, which is a generalization of the structure described in this paper.
15 citations
TL;DR: In this article, it was shown that the set L (R) of all R -linear maps on M n (R ) which preserve both idempotence and nonidempotence is a proper subset of F (R), when the characteristic of R is 2.
13 citations
TL;DR: In this paper, the authors extend this result to freeS-act of infinite rank, where S is any monoid and the self-maps of a set can be written as a product (i.e., composite) of idempotent selfmaps of that set.
Abstract: In 1966, J. M. Howie characterized the self-maps of a set which can be written as a product (i.e., composite) of idempotent self-maps of that set. Using a wreath product construction introduced by V. Fleischer, the first-named author was recently able to describe products of idempotent endomorphisms of a freeS-act of finite rank whereS is any monoid. The purpose of the present paper is to extend this result to freeS-acts of infinite rank.
8 citations
07 Jul 1997
TL;DR: It is proved that the recognizable series are certain rational power series, which can be constructed from the polynomials by using the operations sum, product and a restricted star which is applied only to series for which the elements in the support all have the same connected alphabet.
Abstract: We will describe the recognizable formal power series over arbitrary semirings and in partially commuting variables, i.e. over trace monoids. We prove that the recognizable series are certain rational power series, which can be constructed from the polynomials by using the operations sum, product and a restricted star which is applied only to series for which the elements in the support all have the same connected alphabet. The converse is true if the underlying semi-ring is commutative. Moreover, if in addition the semiring is idempotent then the same result holds with a star restricted to series for which the elements in the support have connected (possibly different) alphabets. It is shown that these assumptions over the semiring are necessary. This provides a joint generalization of Kleene's. Schutzenberger's and Ochmanski's theorems.
8 citations
01 Jan 1997
6 citations
TL;DR: In this paper, it was shown that any unitary commutative locally convex algebra with a continuous product which is a Baire space and in which all entire functions operate is actually m-convex.
Abstract: We show that a unitary commutative locally convex algebra, with a continuous product which is a Baire space and in which entire functions operate is actually m-convex. Whence, as a consequence, the same result of Mitiagin, Rolewicz and Zelazko, in commutative B0-algebras. It is known that entire functions operate in complete m-convex algebras [1]. In [3] Mitiagin, Rolewicz and Zelazko show that a unitary commutative B0-algebra in which all entire functions operate is necessarily m-convex. Their proof is quite long and more or less technical. They use particular properties of B0-algebras, a Baire argument and the polarisation formula. Here we show that any unitary commutative locally convex algebra, with a continuous product which is a Baire space and in which all entire functions operate is actually m-convex. The proof is short, direct and selfcontained. A locally convex algebra (A; ), l. c. a. in brief, is an algebra over a eld K (K = R or C) with a Hausdor locally-convex topology for which the product is separately continuous. If the product is continuous in two variables, (A; ) is said to be with continuous product. A l. c. a. (A; ) is said to bem-convex (l. m. c. a.) if the origin 0 admits a fundamental system of idempotent neighbourhoods ([2]). An
TL;DR: In this article, it was shown that if a finite dimension algebra over an algebraically closed field has projective ideals, then there are infinitely many nonisomorphic indecomposable modules of infinite projective dimension.
Abstract: Let $A$ be a finite dimension algebra over an algebraically closed field such that all its idempotent ideals are projective. We show that if $A$ is representation-infinite and not hereditary, then there exist infinitely many nonisomorphic indecomposable $A$-modules of infinite projective dimension.
Journal Article•
TL;DR: In this paper, the authors give a structure theorem for semigroups of arbitrary cardinality which are semilattices of t-semigroups, groups and PJ-Semigroups each having only one idempotent.
Abstract: We give a structure theorem for semigroups of arbitrary cardinality which are semilattices of t-semigroups, semilattices of groups and semilattices of PJ-semigroups each having only one idempotent.
TL;DR: It is shown that if m is odd then extended m -cycle systems can be equationally defined if and only if m ∈ {3, 5, 7}.
Journal Article•
TL;DR: In this article, a connection between 3-dimensional commutative algebras with trivial trace and plane quartics and their bitangents was made, where the authors showed that the structure of a 3-D algebra on C 3 is called a 3D algebra.
Abstract: We nd a connection between 3-dimensional commutative algebras with trivial trace and plane quartics and their bitangents. In this paper a structure of a commutative algebra on C 3 is called a 3-dimensional algebra. LetA be the set of 3-dimensional algebras. ConsiderA as a linear space. Let A0 A be the linear subspace of algebras with trivial trace. By denition, 2A0 if the contraction of the structure tensor of is equal to zero. By PV we denote the projectivization of a vector space V. For v2 V; v6 0 we denote by v the corresponding point of the projective space PV . Let 2A0 be an algebra with trivial trace. Recall that an element a2 C 3 is called an idempotent if a6 0; a 2 = a. We say that an element a2 P C 3 = P 2 is a generalized idempotent if a 2 = a , where 2 C. Every idempotent denes a generalized idempotent. Every generalized idempotent a2 P 2 such that a 2 6 0 denes uniquely an idempotent a 0 2 C 3 such that a = a 0 . Dene the subscheme X( ) P 2 of the generalized idempotents by the following equation:
TL;DR: This paper shows that in the restricted case of certain binary interval convex primitives, there is a broken symmetry which can be restored by generalizing the state lattice to produce an involution on the important fragment of the narrowing algebra.
Abstract: The narrowing algebra formalism underlying CLP(intervals) consists of lattice-ordered monoids of monotone contractions on the lattice of states; these are generated by the canonical idempotent operators of the primitive relations of the constraint system used for the problem. This mathematical structure has some similarities with that of some classical operator rings, even though the underlying states form a non-Boolean lattice instead of a linear space. In this paper we show that in the restricted case of certain binary interval convex primitives, there is a broken symmetry which can be restored by generalizing the state lattice to produce an involution on the important fragment of the narrowing algebra. This involution allows some basic theorems of classical *-rings to be ported into this domain.
TL;DR: This paper solves the idempotency equation H(x,x)=x for all x∈[0,1] for two special cases when H is a convex linear combination of a strict t-norm and its (1-j)-dual and when F= and its N-dual are aggregation functions.
Abstract: In this paper we deal with the idempotency equation H(x,x)=x for all x∈[0,1]. In particular we solve it for two special cases. First when H is a convex linear combination of a strict t-norm and its (1-j)-dual and second, when H is a convex linear combination of a special kind of aggregation functions F= and its N-dual, being these aggregation functions, called L-representable aggregation functions, a kind of functions verifying a similar representation theorem to the classical representation theorem for non strict Archimedean t-norms.
TL;DR: This paper proves that the identity law axioms in t-norm and t-cornorm are implied by continuity and the other axiomers, and it is proved that the only idempotent t- Normal functions is min (max).
TL;DR: In this paper, a linear map L from M n (R ) to M m (R 1 ) satisfies L ( I n ( R )) I m ( R 1 ), and is called an idempotence preserver.
Abstract: LET R and R 1 be skew-fields with centres F and F 1 , where F F 1 and | F |>2. By M n ( R ) and I n ( R ) we denote the F -space of all n × n matrices over R and the set of all idempotentmatrices in M n ( R ), respectively. If a linear map L from M n ( R ) to M m ( R 1 ) satisfies L ( I n ( R )) I m ( R 1 ) we call L an idempotence preserver (all such maps will be denoted by L n , m ( R , R 1 )). To determine the forms of idempotence preservers is one important content...