DIRECT SUMS OF H-SUPPLEMENTED MODULES

作者：Kuratomi Yosuke^*

来源：Journal of Algebra and Its Applications, 2014, 13(1): 1350075.

DOI：10.1142/S0219498813500758

• (Semi-)lifting module
• H-supplemented module
• internal exchange property
• (weakly) generalized projective

A module M is said to be H-supplemented if, for any submodule X of M, there exists a direct summand M%26apos; of M such that M = X + Y if and only if M = M%26apos; + Y for all Y subset of M (cf. [S. H. Mohamed and B. J. Muller, Continuous and Discrete Modules, London Mathematical Society Lecture Note Series, Vol. 147 (Cambridge University Press, 1999)]). We say that a module M is semi-lifting if any direct summand of M is H-supplemented. A H-supplemented module is a dual to a Goldie-extending module which was introduced by Akalan-Birkenmeier-Tercan [Goldie extending modules, Comm. Algebra 37 (2009) 663-683]. In this paper, we give some characterizations of semi-lifting modules and H-supplemented modules. In addition, we consider generalizations of relative projectivities and apply them to the study of direct sums of semi-lifting modules.

• 出版日期2014-2