Classical quasi-primary submodules

Abstract

In this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. <br /> Then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. In particular, existence and uniqueness of <br /> classical quasi-primary decompositions in finitely generated modules over Noetherian <br /> rings are proved. Moreover, we show that this decomposition and the decomposition into classical primary submodules are the same <br /> when $R$ is a domain with ${rm dim}(R)leq 1$.