φ-Prime and φ-Primary Elements in Lattice Modules

Ashok V. Bingi, C. S. Manjarekar

Abstract

In this paper, we introduce φ-prime and φ-primary  elements in an L-module M. Many of its characterizations and properties are obtained. By counter examples, it is shown that a φ-prime element of M need not be prime, a φ-primary element of M need not be φ-prime, a φ-primary element of M need not be prime and a φ-primary element of M need not be primary. Finally, some results for almost prime and almost primary elements of an L-module M with their characterizations are obtained. Also, we introduce the notions of n-potent prime (respectively n-potent primary) elements in L and M to obtain interrelations among them where n≥2.

 


Keywords

φ-prime element, φ-primary element, almost prime element, almost primary element, n-potent prime element, n-potent primary element

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