On prime element principle in le-modules
نویسندگان
1 School of Mathematics and Statistics, University of Hyderabad, Hyderabad, India.
2 Department of Mathematics, Savitribai Phule Pune University, Maharashtra, India.
3 Department of Mathematics, Savitribai Phule Pune University, Maharashtra, India.
doi
10.22034/as.2025.20866.1687چکیده
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.
