We define and characterize classical completely prime submoduleswhich are a
generalization of both completely prime ideals in rings andreduced modules (as defined by …

Let R be a commutative ring with identity 1\not= 0 1≠ 0 and let I be a proper ideal of R. DD
Anderson and E. Smith called I weakly prime if a, b ∈ R a, b∈ R and 0\not= ab ∈ I 0≠ ab∈ …

Let I be an ideal of a ring R. Consider the following conditions on R: 1. If X is a finitely
generated submodule of a finitely generated projective module P, then X= A⨁ B where is a …

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 …

Let R be a ring with identity and let M be a unital left R-module. A proper submodule L of M
is radical if L is an intersection of prime submodules of M. Moreover, a submodule L of M is …

On Unions of Prime Submodules Page 1 Southeast Asian Bulletin of Mathematics (2004) 28:
213-218 Southeast Asian Bulletin of Mathematics © SEAMS, 2004 On Unions of Prime …

S-PRIME IDEALS IN PRINCIPAL DOMAIN Page 1 J. Indones. Math. Soc. Vol. 29, No. 01 (2023),
pp. 93–98. S-PRIME IDEALS IN PRINCIPAL DOMAIN Mohamed Aqalmoun 1 1Department of …

Prime submodules and prime modules have appeared in many contexts. Modifying the
structure of prime ideals, many authors want to transfer this notion to right or left modules …