… We define a prime FM-module for a F-ring M. It is shown that a subset P of M is a prime ideal
… Although all the results in this paper involve only right modules and the right operator ring of …

… ring R9 let R1 =R when le R; if l φ R, adjoin an identity s usual by R1 = Z χR, Z =0, ±1, ±2, ....
A submodule Κα M of a right -module M is prime if for … ways of defining a prime module, all of …

… and obtained various generalizations analogous of corresponding parts in ring … prime Γ-rings.
Main results are the following theorems: (1) A Γ-ring M is a subdirect sum of prime Γ-rings if …

… the concept of a gamma modules in R investigate at some such modules. In this regard, we
… phism of a gamma modules and give the related basic results of a gamma modules. In 2005, …

… over R and studied the essential properties of such modules. In this regard, we look at
gamma R-module R-submodules and homomorphism, as well as some simple gamma R-module …

… make of N an M/AM(N)-module … Let R be the right operator ring of M. The ordinary ring
theory shows that J(R) is a rqr ideal of R and contains all the rqr right ideals of R (cf, [7] p. 12). As …

… ^ ί sa right 22-module, and we call 22 the right operator ring of the Γring Λf. … Prime ideals in
matrix gamma rings* We note that Lemma 1 and Theorem 1 hold also for the matrix ΓΛ,m-ring …

… ring is also a generalization of the concept of near-ring. The object of the present paper is
to introduce the concept of module over a Γ-near-ring… G is a module over a Γ-near-ring M) …

… -prime gamma rings. Main results are the following theorems: (1) Let M be a semi-prime I-ring
and Q a quotient I-ring … the mapping ) is a right M-module injective homomorphism and so …

… rings, anything that can be done conveniently without the concept of "injectivity." In Chapter
Four, injective modules and rings … of Proposition 7 of Section 1.2 for modules instead of rings: …