Singh, Abhay K. Essentially slightly compressible modules and rings. (English) Zbl 1258.16009 Asian-Eur. J. Math. 5, No. 2, 1250028, 8 p. (2012). 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. Cited in 2 Documents 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) Keywords:essential modules; uniform modules; essentially compressible modules; slightly compressible modules; V-rings; nonsingular injective modules; slightly compressible rings Citations:Zbl 1114.16007 PDFBibTeX XMLCite \textit{A. K. Singh}, Asian-Eur. J. Math. 5, No. 2, 1250028, 8 p. (2012; Zbl 1258.16009) Full Text: DOI References: [1] DOI: 10.1007/978-1-4684-9913-1 · doi:10.1007/978-1-4684-9913-1 [2] Dung N. V., Extending Modules (1994) · Zbl 0841.16001 [3] Khuri S. M., J. Algebra 59 pp 401– · Zbl 1095.14057 [4] Pandeya B. M., Indian Math. Soc. pp 121– [5] DOI: 10.1016/j.jpaa.2004.09.001 · Zbl 1087.16001 · doi:10.1016/j.jpaa.2004.09.001 [6] DOI: 10.1016/j.jalgebra.2005.08.018 · Zbl 1114.16007 · doi:10.1016/j.jalgebra.2005.08.018 [7] DOI: 10.1080/00927870802110854 · Zbl 1155.16004 · doi:10.1080/00927870802110854 [8] Tiwary A. K., Progr. Math. 5 pp 49– [9] DOI: 10.1090/S0002-9904-1976-14093-1 · Zbl 0329.16006 · doi:10.1090/S0002-9904-1976-14093-1 [10] DOI: 10.1090/S0002-9939-1976-0419512-6 · doi:10.1090/S0002-9939-1976-0419512-6 [11] J. Zelmanowitz, Ring Theory II (Marcel Dekker, NY, 1977) pp. 281–294. [12] DOI: 10.1080/00927878108822561 · Zbl 0469.16004 · doi:10.1080/00927878108822561 [13] DOI: 10.1080/00927879308824653 · Zbl 0791.16002 · doi:10.1080/00927879308824653 [14] Zhou Y., Bull. Aust. Math. Soc. 53 pp 517– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.