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Essentially slightly compressible modules and rings. (English) Zbl 1258.16009

Summary: The concepts of essentially slightly compressible modules and essentially slightly compressible rings are introduced, and related properties are investigated. The notion of essentially slightly compressible modules and rings are generalization of essentially compressible modules and rings introduced by P. F. Smith and M. R. Vedadi, [J. Algebra 304, No. 2, 812-831 (2006; Zbl 1114.16007)]. Also provided is the characterization of such modules in terms of nonsingular injective modules. It is shown that over a Noetherian ring for a uniform module, essentially slightly compressible modules, slightly compressible modules and nonzero homomorphism from \(M\) into \(U\) for a nonzero uniform submodule \(U\) of \(M\) are equivalent. Throughout this paper, all rings are associative and all modules are unital right \(R\)-modules.

MSC:

16D80 Other classes of modules and ideals in associative algebras
16D50 Injective modules, self-injective associative rings
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)

Citations:

Zbl 1114.16007
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References:

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