On the interior of a submodule with respect to a set of ideals

Abstract

In this paper, we investigate interior operations on submodules and introduce a new interior operation by using a certain submodule class. Let R be a commutative ring with identity and I be a set of ideals of R. We define I-second submodules and I-interior of a submodule. We show that second, secondary and strongly second submodules are special types of I-second submodules. We investigate several properties of I-interiors of submodules and give a concrete expression of I-interior of a submodule of an Artinian module. We use the concept of I-interior of a submodule to find some results on I-second submodules and attached primes of an Artinian module.

Mathematics Subject Classification (2010): 13A15, 13C13, 13C99.

Keywords: I-second submodule, interior operation, I-interior of a submodule, attached prime ideal