Bases in semilinear spaces over join-semirings

被引：12

作者：

Zhao, Shan ^{[1
]}

Wang, Xue-ping ^{[1
]}

机构：

[1] Sichuan Normal Univ, Coll Math & Software Sci, Chengdu 610066, Sichuan, Peoples R China

来源：

FUZZY SETS AND SYSTEMS | 2011年 / 182卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Semiring; Join-semiring; Semi linear space; Basis; MAX-ALGEBRA;

D O I：

10.1016/j.fss.2010.10.013

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper investigates the cardinality of a basis in semilinear spaces of n-dimensional vectors over join-semirings. First, it introduces the notion of an irredundant decomposition of an element in a join-semiring, then discusses the cardinality of a basis and proves that the cardinality of each basis is n if and only if the multiplicative identity element 1 is join-irreducible. If 1 is not a join-irreducible element then each basis need not have the same number of elements in semilinear spaces of n-dimensional vectors over join-semirings. This gives an answer to an open problem raised by Di Nola et al. in their work [Algebraic analysis of fuzzy systems, Fuzzy Sets and Systems 158 (2007) 1-22]. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：93 / 100

页数：8

共 14 条

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