ABSORBING ELEMENTS IN LATTICE MODULES

Year 2016, Volume: 19 Issue: 19, 58 - 76, 01.06.2016

C. S. Manjarekar A. V. Bingi

https://doi.org/10.24330/ieja.266193

Cited By: 2

Abstract

In this paper we introduce and investigate 2-absorbing, n-absorbing,
(n, k)-absorbing, weakly 2-absorbing, weakly n-absorbing and weakly (n, k)-
absorbing elements in a lattice module M. Some characterizations of 2-
absorbing and weakly 2-absorbing elements of M are obtained. By counter
example it is shown that a weakly 2-absorbing element of M need not be 2-
absorbing. Finally we show that if N ∈ M is a 2-absorbing element, then
rad(N) is a 2-absorbing element of M.

Keywords

2-absorbing element, n-absorbing element, (n, k)-absorbing element, weakly 2-absorbing element, rad(N)