Published: 2024-03-20

Closure operations on Intuitionistic Linear algebras

Y. L. Tenkeu Jeufack Logo ORCID , E. R. Alomo Temgoua , O. A. Heubo-Kwegna

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.

Download files

Citation rules

Tenkeu Jeufack, Y. L., Alomo Temgoua, E. R., & Heubo-Kwegna, O. A. (2024). Closure operations on Intuitionistic Linear algebras. Annales Mathematicae Silesianae, 38(2), 351–380. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/17252

Vol. 38 No. 2 (2024)
Published: 2024-07-23


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

This website uses cookies for proper operation, in order to use the portal fully you must accept cookies.