Homological dimension of Rees matrix semigroups in intelligent fuzzy systems

Issue title: Special Section: Fuzzy theoretical model analysis for signal processing

Guest editors: Valentina E. Balas, Jer Lang Hong, Jason Gu and Tsung-Chih Lin

Article type: Research Article

Authors: Cui, Ranran^{a; b; *}

Affiliations: [a] College of Science, Henan University of Technology, Zhengzhou, China | [b] Institute of Mathematics, University of Tartu, Tartu, Estonia

Correspondence: [*] Corresponding author. Ranran Cui. E-mail: ranrancui1702@yeah.net.

Abstract: We shall consider intelligent homological dimensions of 0-direct union of finite Rees matrix semigroups. First we give some characterizations of Rees matrix semigroup algebras. Then if K is a ring and S has a Rees matrix ideal M, we give the bounds of r.gl.dim K[S] in terms of r.gl.dim K [Ti] and r.gl.dim K[S/M]. The bounds for r.gl.dim K[S] are given, supposing that the finite monoid S is a 0-direct union of some finite Rees matrix semigroups which are in forms of Si = M (Ti ; Ii ; Λi ; Pi). In addition, it is determined that K[S] has finite homological dimension if and only if each Ti has finite homological dimension.

Keywords: Homological dimension, *-ideal chain, primitively decomposable abundant semigroups, inverse semigroup, intelligent

DOI: 10.3233/JIFS-179313

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 4779-4783, 2019