On prime element principle in le-modules

Articles in Press

Document Type : Research Paper

Authors

1 School of Mathematics and Statistics, University of Hyderabad, Hyderabad, India.

2 Department of Mathematics, Savitribai Phule Pune University, Maharashtra, India.

Abstract

In this article, we have extended the notion of Oka families for commutative rings and modules to le-modules. We have introduced prime element principle, stated as, for a particular family F of submodule elements of an le-module M, submodule element maximal in terms of not belonging to F is prime. As a consequence, many results about the existence of prime elements of le-modules have been established. Furthermore, we have provided a method for constructing prime elements in le-modules and proved the existence of maximal m-systems, which is employed to characterize minimal prime elements.

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References

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Algebraic Structures and Their Applications

Articles in Press, Corrected Proof
Available Online from 27 February 2025

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