ON (n -1; n)-phi-m-PRIME AND (n -1; n)-WEAKLY PRIME SUBMODULES

Abstract

Abstract. Let m; n ≥ 2 be two positive integers, R a commutative<br /> ring with identity and M a unitary R-module. A proper<br /> submodule P of M is an (n 􀀀 1; n)-Φm-prime ((n 􀀀 1; n)-weakly<br /> prime) submodule if a1; : : : ; an􀀀1 2 R and x 2 M together with<br /> a1 : : : an􀀀1x 2 Pn(P : M)m􀀀1P (0 ̸= a1 : : : an􀀀1x 2 P) imply<br /> a1 : : : ai􀀀1ai+1 : : : an􀀀1x 2 P, for some i 2 f1; : : : ; n􀀀1g or a1:::an􀀀1 2<br /> (P : M). In this paper we study these submodules. Some useful<br /> results and examples concerning these types of submodules are<br /> given.