On Generalizations of Classical Prime Elements of Lattice Modules

On Generalizations of Classical Prime Elements of Lattice Modules

  • Pradip Girase K K M College, Manwath, Parbhani 431505, India.
  • Vandeo Borkar Yeshwant mahavidyalaya, Nanded, India.
  • Narayan Phadatare

Abstract

Let $M$ be a lattice module over a $C-$lattice $L$ and $\phi \colon M\to M$ be a function on $M$ such that $\phi(N)\leq N$ for each $N\in M$. In this paper, we introduce the concept of an $(n-1, n)-\phi-$classical prime element in a lattice module $M$. A proper element $P$ of $M$ is called an $(n-1, n)-\phi-$classical prime element, if $a_{1}\cdots a_{n-1}X\leq P, a_{1}\cdots a_{n-1}X\nleq \phi(P)$ implies $a_{1}\cdots a_{i-1}a_{i+1}\cdots a_{n-1}X\leq P$, for some $i\in \{1, \cdots, n-1\}$$(n\geq 3)$, for all $a_{1}, \cdots, a_{n-1}\in L$ and $X\in M$. Further, we study various characterizations of these elements.


 

Published
2020-09-01
How to Cite
GIRASE, Pradip; BORKAR, Vandeo; PHADATARE, Narayan. On Generalizations of Classical Prime Elements of Lattice Modules. Eurasian Bulletin of Mathematics (ISSN: 2687-5632), [S.l.], v. 3, n. 2, p. 73-83, sep. 2020. ISSN 2687-5632. Available at: <http://www.ebmmath.com/index.php/EBM/article/view/57>. Date accessed: 21 oct. 2020.