Multiplication Modules and Homogeneous Idealization III
نویسنده
چکیده
In our recent work we gave a treatment of certain aspects of multiplication modules, projective modules, flat modules and cancellation-like modules via idealization. The purpose of this work is to continue our study and develop the tool of idealization, particularly in the context of closed, divisible injective, and simple modules. We determine when a ring R (M), the idealization of M , is a quasi-Frobenius or a distinguished ring. We also introduce and investigate the concept of M 2 (weak) cancellation ideals. MSC 2000: 13C13, 13C05, 13A15
منابع مشابه
Multiplication Modules and Homogeneous Idealization II
All rings are commutative with identity and all modules are unital. Let R be a ring, M an R-module and R(M), the idealization of M . Homogenous ideals of R(M) have the form I (+)N , where I is an ideal of R and N a submodule of M such that IM ⊆ N . A ring R (M) is called a homogeneous ring if every ideal of R (M) is homogeneous. In this paper we continue our recent work on the idealization of m...
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