Showing papers on "Idempotence published in 1987"
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355 citations
TL;DR: In this paper, the authors characterize linear mappings L on U that satisfy one of the following properties: (i) L(adjA)=adjL(A) for all A in U; (ii) L preserves idempotent matrices, and L(In)=In, where F is the real field R or the complex field C.
42 citations
TL;DR: In this paper, it was shown that the lattice generated by a set of mutually annihilating primitive idempotents is an anti-involution such that each symmetric elements is either a nilpotent or then some right multiple of it is a nonzero symmetric idemomorphism.
Abstract: Spinor spaces can be represented as minimal left ideals of Clifford algebras and they are generated by primitive idempotents. Primitive idempotents of the Clifford algebras Rp, q are shown to be products of mutually nonannihilating commuting idempotent % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabaGaaiaacaqabeaadaqaaqGaaO% qaamaaleaaleaacaaIXaaabaGaaGOmaaaaaaa!3DBD!\[{\textstyle{1 \over 2}}\]2}}\](1+eT), where the k=q−rq−p basis elements eT satisfy eT2=1. The lattice generated by a set of mutually annihilating primitive idempotents is examined. The final result characterizes all Clifford algebras Rp, q with an anti-involution such that each symmetric elements is either a nilpotent or then some right multiple of it is a nonzero symmetric idempotent. This happens when p+q<-3 and (p, q)≠(2, 1).
29 citations
28 Sep 1987
TL;DR: A complete unification algorithm for idempotent functions is presented and an improvement of the universal algorithm is shown that is derived from the universal unification algorithm, which is based on the narrowing process.
Abstract: A complete unification algorithm for idempotent functions is presented. This algorithm is derived from the universal unification algorithm, which is based on the narrowing process. First an improvement of the universal algorithm is shown. These results are applied to the special case of idempotence resulting in an idempotence unification algorithm.
21 citations
TL;DR: This article classified all varieties of idempotent semigroups with respect to the unification types of their defining sets of identities and showed that all of them are of unification type zero.
Abstract: We have classified all varieties of idempotent semigroups with respect to the unification types of their defining sets of identities. With the exception of eight finitary unifying theories these are all of unification type zero. This yields countably many examples of theories of that type which are more “natural” than the first example constructed by Fages and Huet [9, 10].
16 citations
7 citations
TL;DR: The probability that the product of l square matrices of size n over a finite field with q elements will be nilpotent is shown to be 1-[( q n -1)/ q n ] l.
4 citations
TL;DR: A construction of all globally idempotent semigroups with Boolean (complemented modular, relatively complemented, sectionally complemented) congruence lattice is given in this paper.
Abstract: A construction of all globally idempotent semigroups with Boolean (complemented modular, relatively complemented, sectionally complemented, respectively) congruence lattice is given. Furthermore, it is shown that an arbitrary semigroup has Boolean (...) congruence lattice if and only if it is a special kind of inflation of a semigroup of the foregoing type. As applications, all commutative, finite, and completely semisimple semigroups, respectively, with Boolean (...) congruence lattice are completely determined.
2 citations
Journal Article•
TL;DR: In this paper, the authors introduce a new class of locally-convex algebras containing the one of unital uniformly uniformly $A$-convariant (i.e., with $m$-bounded bases).
Abstract: In this paper, we introduce a new class of locally-convex algebras containing the one of unital uniformly $A$-convex algebras. It is the collection of those separated locally-convex algebras which have an algebraic basis whose idempotent hull is bounded. Such algebras are said to be “with $m$- bounded bases”. Under different notions of completeness, we endow these algebras with a complete algebra norm which has the same bounded sets of different kinds. Different questions on the factorization and commutativity are considered.
1 citations
07 Sep 1987
TL;DR: This analysis has shown that there are several levels of ideas used in categories of Park-Milner processes, and the theory of exact categories provides the fundamental structures.
Abstract: This analysis has shown that there are several levels of ideas used in categories of Park-Milner processes. First and foremost, the theory of exact categories provides the fundamental structures. Second, the idea of rooted processes means one is attempting to work in a bigpointed category. As this brief analysis shows, bipointed categories have a rather weak collection of nice properties—at least known to me. Third, additive idempotence introduces considerable additional structure, and it is here that the non-unital aspects of the A-modules play an important role.