We investigateϕ-prime andϕ-primary elements in a compactly generated multiplicative latticeL. By a counterexample, it is shown that aϕ-primary element inLneed not be primary. Some characterizations ofϕ-primary andϕ-prime elements inLare obtained. Finally, some results for almost prime and almost primary elements inLwith characterizations are obtained.
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 .Mathematics Subject Classification (2010): 06D10, 06E10, 06E99, 06F99
We introduce the concept “An element weakly primary to another element” and using this concept we have generalized some result proved by Manjarekar and Chavan (2004). It is shown that if is a family of elements weakly primary to a in L, then is weakly primary to a.
We obtain some elementary residuation properties in lattice modules and obtain a relation between a weakly primary element in a lattice moduleMand weakly prime element of a multiplicative latticeL.
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