Let R be a commutative ring with identity. The purpose of this paper is to introduce a new
class of modules over R called primeful R-modules. Every nonzero primeful module …

WEAKLY PRIME SUBMODULES AND PRIME SUBMODULES Page 1 Glasgow Math. J. 48 (2006)
343–346. C 2006 Glasgow Mathematical Journal Trust. doi:10.1017/S0017089506003119 …

Let B be a submodule of an R-module M. The intersection of all prime submodules of M
containing B is denoted by rad (B). For every positive integer n, a generalization of E (B) …

Throughout this paper all rings are commutative with identity and all modules are unitary. A
proper submodule N of a module M over a ring R is said to be prime (P-prime) if ra∈ N for …

Let M be a module over a commutative ring R. A submodule P of M is called prime if P≠ M
and, whenever r∈ R, e∈ M, and re∈ P, we have rM⊆ P or e∈ P. We let Spec (M) denote …

In this paper, we study the dimension of a module over a commutative ring, which is defined
to be the length of a longest chain of prime submodules. This notion is analogous to the …

PRIME SUBMODULES OF ARTINIAN MODULES Page 1 TAIWANESE JOURNAL OF
MATHEMATICS Vol. 13, No. 6B, pp. 2011-2020, December 2009 This paper is available online at …

Prime Submodules and Flat Modules Page 1 Acta Mathematica Sinica, English Series Jan.,
2007, Vol. 23, No. 1, pp. 147–152 Published online: Sep. 15, 2006 DOI: 10.1007/s10114-005-0813-0 …

Let R be a commutative ring with identity, and let n> 1 be an integer. A proper submodule N
of an R-module M will be called 2-absorbing [resp. n-weakly prime], if r; s 2 R and x 2 M with …

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