A boolean transfer principle from L*-Algebras to AL*-Algebras

Just as Kaplansky [4] has introduced the notion of an AW*-module as a generalization of a complex Hilbert space, we introduce the notion of an AL*-algebra, which is a generalization of that of an L*-algebra invented by Schue [9, 10]. By using Boolean valued methods developed by Ozawa [6–8], Takeuti [11–13] and others, we establish its basic properties including a fundamental structure theorem. This paper should be regarded as a continuation or our previous paper [5], the familiarity with which is presupposed. MSC: 03C90, 03E40, 17B65, 46L10.     

I—ring which Satisfies A.D.C.C on Principal Left Ideals

Derndtl0n1AringRiscalledI-ring,ifasasemigroupRisgeneratedbyitsidemPOtentelements.Defhotl0n2AringRissaidtosatisfyalm0stdescending(0rascending)chaincondi-tionsonleftideals,ifforeverydescending(ascending)chainofleftideals0fR,I,nI2n...nI.Xi..-(I,GI2G...GI'g..-),thereexistsaPOsitiveintegerpsuchthatRPI=Ii(IiGR-'I,)foralli,whereR-'I,={ueRlR'u=IP}.By[5JitisknownthatAringRsatisfiesA.D.C.C(OTA.A.C,C)onleftidealsifandonlyifforeverydescending(0rascending)chalnOfleftidealsofR,I,nI2n-..n…     

地下水污染评价的模糊综合聚类法

本文将模糊聚类最大矩阵元原理与基于数据迭代为基础的水质模糊评价理论模型相结合．形成模糊综合聚类法．利用该方法对甘肃金昌市地下水水质进行了分类评价．得到今人满意的结果。     

Boolean sublattices connected with minimization problems on matroids

It is noted that the decomposition of a network presented by J.C. Picard and M. Queyranne through an algorithmic argument may be defined from a general lattice-theoretic result for more general problems for which the equalities of maximum-flow minimum-cut type hold.     

On the generalized indices of boolean matrices

We characterize completely those Boolean matrices with the largest generalized indices in the class of Boolean matrices and in the class of reducible Boolean matrices and derive a new upper bound for the generalized index in terms of period. We also generalize the upper and lower multiexponents of primitive Boolean matrices to general Boolean matrices.     

Studying Non-negative Factorizations with Tools from Linear Algebra over a Semiring

We develop the technique useful for studying the problem of factoring nonnegative matrices. We illustrate our method, based on the tools from linear algebra over a semiring, by applying it to studying the problem of existence of a rank-three matrix with full nonnegative rank equal to n.     

Boole–De Morgan Algebras and Quasi-De Morgan Functions

In this paper we establish a Stone-type and a Birkhoff-type representation theorems for Boole–De Morgan algebras and prove that the free Boole–De Morgan algebra on n free generators is isomorphic to the Boole–De Morgan algebra of quasi-De Morgan functions of n variables. Also we introduce the concept of Zhegalkin polynomials for quasi-De Morgan functions and consider the representation problem of those functions by polynomials.     

Boolean Metric Spaces and Boolean Algebraic Varieties

Abstract

The concepts of Boolean metric space and convex combination are used to characterize polynomial maps A ⁿ ?→?A ^m in a class of commutative Von Neumann regular rings including p-rings, that we have called CFG-rings. In those rings, the study of the category of algebraic varieties (i.e., sets of solutions to a finite number of polynomial equations with polynomial maps as morphisms) is equivalent to the study of a class of Boolean metric spaces, that we call here CFG-spaces.