… Then nilrad(M) = p is a prime ideal and M is called p-secondary. The purpose of this
paper is to introduce second submodules (the dual notion of prime submodules). The non-zero …

… submodule of M is sum-irreducible (see Theorem 2.12). In Section 3, we introduce the dual
notion of isolated submodules (… useful characterizations for coisolated submodules of M (see …

… for second submodules (see Theorem 2.10). In Section 3, we will introduce a dual notion of
… if M does not have any second submodule or for every second submodule S of M there exists …

… a prime module. The intersection of all prime submodules of a module M is called the prime
… We define the notion of m ⁎ -system set which is the dual notion of m-system set defined in […

… In this article, we introduce the dual notions of strongly prime, weakly prime, semiprime,
and primal submodules, that is, strongly second, weakly second, semisecond, and secondal …

… generalize the notion of prime ideal. Consequently, there is defined prime module and its
dual, … Every characteristic 2-prime submodule is l-prime. Proof. Let N be a characteristic 2-…

… In this paper, we will study the dual notion of prime radicals (that is, second socles) of
submodules of M and obtain some related results. … In [13], Yassemi introduced the dual …

… submodules, as a dual of prime submodules, was first introduced by Yassemi [4]. A non-zero
submodule N … Furthermore, we introduce the notion of minimal fuzzy submodules and prove …

… notion of strongly prime submodules and show that if there exists a non-zero module over a
primary ring that is both projective and injective, then the ring has only one prime … the dual of …

… submodule if M/P is a prime module. As a dual notion of prime submodules, Yassemi [24]
introduced the notion of second submodules of a given non-zero module over a commutative …