Classical quasi-primary submodules

Document Type : Research Paper



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