<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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 <bold>L</bold> is used to study the unifying properties of some subclasses of the lattice of filters of <bold>L</bold>. In particular, we obtain that for a stable closure operation <italic>c</italic> on an IL-algebra, the collection of <italic>c</italic>-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.</p>
</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.

Closure Operations on Intuitionistic Linear Algebras

University of Yaoundé 1, Faculty of Sciences

University of Yaoundé 1, Ecole Normale Supérieure de Yaoundé

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Closure Operations on Intuitionistic Linear Algebras"}

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...

Closure Operations on Intuitionistic Linear Algebras

Published Online: Mar 20, 2024

Page range: 351 - 380

Received: Apr 03, 2023

Accepted: Feb 05, 2024

DOI: https://doi.org/10.2478/amsil-2024-0007

Keywords
IL-algebra, closure operation, extended filter, prime filter

© 2024 Y.L.Tenkeu Jeufack et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Closure Operations on Intuitionistic Linear Algebras

Published Online: Mar 20, 2024

Page range: 351 - 380

Received: Apr 03, 2023

Accepted: Feb 05, 2024

DOI: https://doi.org/10.2478/amsil-2024-0007

KeywordsIL-algebra, closure operation, extended filter, prime filter

© 2024 Y.L.Tenkeu Jeufack et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
IL-algebra, closure operation, extended filter, prime filter