C. S. Manjarekar | Searcharxiv

arXiv2020

Pseudo-Primary, Classical Prime and Pseudo-Classical Primary Elements in Lattice Modules

In this paper, we introduce the notion of pseudo-primary elements and pseudo-classical primary elements in an $L$-module $M$ and obtain their characterizations. The aim of the paper is to show $rad(N)\in M$, the radical of $N\in M$ is prime if $N$ is either pseudo-primary or pseudo-classical primary. Also, we study classical prime elements of an $L$-module $M$ to obtain many of its characterizations and its properties.

math.RA↗

arXiv2020

$\displaystyle δ$-Primary Elements In Lattice Modules

In this paper, we introduce the expansion function $δ$ on an $L$-module $M$. We define and investigate a $δ$-primary element in an $L$-module $M$. Its characterizations and many of its properties are obtained. $δ_0$-primary and $δ_1$-primary elements of an $L$-module $M$ are related with 2-absorbing, 2-absorbing primary elements of an $L$-module $M$ to obtain their special properties. The element $δ_1(N)\in M$ is related to $rad(N)\in M$, the radical element of $M$ to obtain its properties where $N\in M$. We define a $δ_L$-primary element in an $L$-module $M$ where $δ_L$ is an expansion function on $L$ and find relation among a $δ_L$-primary element of $M$ and its corresponding $δ_L$-primary element of $L$.

math.RA↗