If M is a torsion-free module over an integral domain, then we show that for each submodule
N of M the envelope EM (N) of N in M is an essential extension of N. In particular, if N is …

The purpose of the present paper is to prove some properties of the strongly irreducible
submodules in the arithmetical and Noetherian modules over a commutative ring. The …

Throughout this paper, all rings considered are integral domains, the dimension of a ring R,
denoted dimR, means its Krull dimension, and all module are unital. Let R be a ring and M …

In most cases, almost prime submodules are equivalent to prime submodules, but in a
finitely generated module, it is not necessarily equivalent. Based on the fact that a finitely …

It is shown that if R is an integral domain with| R|= 2ʿ, then either R has a maximal subring
or R has a prime ideal P which is not a maximal ideal of R, Char (R/P)= Char (R) and| R/P|< …

If R is a simple ring with 1 which contains a maximal annihilator right ideal then R is the
endomorphism ring of a unital torsion-free module over an integral domain. We first prove …

In this paper we generalize to modules of singular submodule zero over a ring of singular
ideal zero some of the results, which are well known for torsion-free modules over a …

Let R be a ring with 1 E R. In Mod-R the total Tot (M, N) is a semi-ideal, which contains the
radical Rad (M, N), the singular ideal tl (M, N) and the cosingular ideal V'(M, N). We study …

Let R be an arbitrary ring, M a rightR-module and S= EndR (M), the endomorphism ring of M.
A proper fully invariant submodule X of M is called a prime submodule of M if for any ideal I …

It is known that every semiprime ring is a subdirect sum of prime rings. This is a
consequence of the fact that every semiprime ideal is an intersection of prime ideals. We aim …