Closure Operations on Intuitionistic Linear Algebras-Reference-Cited by-同舟云学术

Closure Operations on Intuitionistic Linear Algebras

Published:2024-03-20 Issue:2 Volume:38 Page:351-380
ISSN:2391-4238
Container-title:Annales Mathematicae Silesianae
language:en
Short-container-title:

Author:

Tenkeu Jeufack Y.L.¹^ORCID,Alomo Temgoua E.R.²,Heubo-Kwegna O.A.³

Affiliation:

1. University of Yaoundé 1, Faculty of Sciences , Department of Mathematics , Cameroon

2. University of Yaoundé 1, Ecole Normale Supérieure de Yaoundé , Department of Mathematics , Cameroon

3. Department of Mathematical Sciences , Saginaw Valley State University , 7400 Bay Road, University Center, MI 48710 , USA

Abstract

Abstract In this paper, we introduce the notions of radical filters and extended filters of Intuitionistic Linear algebras (IL-algebras for short) and give some of their properties. The notion of closure operation on an IL-algebra is also introduced as well as the study of some of their main properties. The radical of filters and extended filters are examples of closure operations among several others provided. The class of stable closure operations on an IL-algebra L is used to study the unifying properties of some subclasses of the lattice of filters of L. In particular, we obtain that for a stable closure operation c on an IL-algebra, the collection of c-closed elements of its lattice of filters forms a complete Heyting algebra. Hyperarchimedean IL-algebras are also characterized using closure operations. It is shown that the image of a semi-prime closure operation on an IL-algebra is isomorphic to a quotient IL-algebra. Some properties of the quotients induced by closure operations on an IL-algebra are explored.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/amsil-2024-0007

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