scispace - formally typeset
Search or ask a question

Showing papers on "Idempotence published in 1975"


Journal ArticleDOI
TL;DR: A number of papers have appeared with the purpose of generalizing Albert's long-standing result that a simple right alternative algebra of finite dimension over a field of characteristic f 2 that has a unit element e and an idempotent c # e is necessarily alternative as discussed by the authors.

52 citations



Journal ArticleDOI
TL;DR: In this article, a right alternative ring R having an idempotent c decomposes into a direct sum R = RI1 + R,, + R+R+R, + R + R, of submodules, its Peirce decomposition with respect to c. Partial results along these lines have been obtained earlier by Hentzel, Humm, Kleinfeld, Maneri, Sterling and the author.

10 citations



Journal ArticleDOI
TL;DR: In this paper, a method for the construction of essentially idempotent and Hermitian diagonal elements of the matric algebra of the permutation group Sn is proposed, which is applied to a 7-electron system in the spin state S = MS = 1/2 and the results are listed in the Appendix.
Abstract: A method for the construction of the essentially idempotent and Hermitian diagonal elements of the matric algebra of the permutation group Sn is proposed. For the irreducible representation [λ] = [λ1, λ2] characterising a spin state S of an n-electron system, it is found that this method generates the complete set of spin projections from the appropriate primitive spin functions. The method is applied to a 7-electron system in the spin state S = MS = 1/2 and the results are listed in the Appendix.

5 citations






Journal ArticleDOI
TL;DR: In this paper, it is shown that there exists an isomorphism between the space of E-valued functions on a semigroup T of semicharacters on an idempotent semigroup S into a locally convex space E. The space of functions on T which are absolutely continuous with respect to a positive definite function F and the operators on this set of fmitely additive measures on a certain algebra of subsets of S are derived.
Abstract: Let E be a locally convex space and let T be a semigroup of semicharacters on an idempotent semigroup. It is shown that there exists an isomorphism between the space of E-valued functions on T and the space of all E-valued finitely additive measures on a certain algebra of sets. The space of all E-valued functions on T which are absolutely continuous with respect to a positive definite function F is identified with the space of all E-valued measures which are absolutely continuous with respect to the measure mF corresponding to F. Finally a representation is given for the operators on the set of all E-valued finitely additive measures on an algebra of sets which are absolutely continuous with respect to a positive measure. Introduction. Functions of bounded variation and absolutely continuous functions have been studied by several authors including [1], [2], [5], [6], [7], [8] and [9]. In [6] a representation is obtained of the linear functionals on AC(J) which are continuous in the bounded-variation norm in terms of the vintegral. In [8] and [9] the concepts of bounded variation and absolutely continuous are developed on idempotent semigroups. In [1] and [2] the results of [8] and [9] are used to extend the v-integral characterization of functionals in [6] to a v-integral characterization of normed vector space-valued operators on normed vector space-valued absolutely continuous functions on an idempotent semigroup. In this paper we study the space of functions from a semigroup T of semicharacters on an idempotent semigroup S into a locally convex space E. We identify E-valued functions on T with E-valued finitely additive measures on a certain algebra of subsets of S, and then represent operators on this set of fmitely additive measures. To this end we adopt the notation and development in [8] and [9]. Received by the editors May 15, 1973 and, in revised form, March 10, 1974. AMS (MOS) subject classifications (1970). Primary 46G10, 46E40; Secondary 28A25, 28A45.