Document Type : Other
Authors
1 Department of Mathematics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan , P.O.Box 518, Rafsanjan, Iran
2 Department of Mathematics, Faculty of Sciences, Shahid Bahonar University of Kerman, Kerman, Iran.
Abstract
Abstract. Let m; n ≥ 2 be two positive integers, R a commutative
ring with identity and M a unitary R-module. A proper
submodule P of M is an (n 1; n)-Φm-prime ((n 1; n)-weakly
prime) submodule if a1; : : : ; an1 2 R and x 2 M together with
a1 : : : an1x 2 Pn(P : M)m1P (0 ̸= a1 : : : an1x 2 P) imply
a1 : : : ai1ai+1 : : : an1x 2 P, for some i 2 f1; : : : ; n1g or a1:::an1 2
(P : M). In this paper we study these submodules. Some useful
results and examples concerning these types of submodules are
given.
Keywords