Prime and primary ideals on L-algebras

Articles in Press

Document Type : Research Paper

Authors

Soft Computing Center, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.

Abstract

In this paper, we review L-algebras and CL-algebras, focusing in particular on the notion of a prime ideal. We establish criteria for a prime ideal and analyze the relationship between maximal and prime ideals. In addition, we define prime ideals in CL-bounded algebras, and state conditions for an ideal to be prime in a self-distributing bounded L-algebra. We introduce the radical of an ideal and show that if its radical is maximal, then it is a prime ideal. Finally, we establish conditions under which every prime ideal in an L-algebra is primary.

Keywords

References

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Algebraic Structures and Their Applications

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Available Online from 27 February 2025

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