Z-Small Submodules and Z-Hollow Modules
Keyword(s):
A submodule Ϝ of an R-module Ε is called small in Ε if whenever , for some submodule W of Ε , implies . In this paper , we introduce the notion of Ζ-small submodule , where a proper submodule Ϝ of an R-module Ε is said to be Ζ-small in Ε if , such that , then , where is the second singular submodule of Ε . We give some properties of Ζ-small submodules . Moreover , by using this concept , we generalize the notions of hollow modules , supplement submodules, and supplemented modules into Ζ-hollow modules, Ζ-supplement submodules, and Ζ-supplemented modules. We study these concepts and provide some of their relations .
2011 ◽
Vol 2011
◽
pp. 1-12
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2017 ◽
Vol 9
(2)
◽
pp. 57-70
2013 ◽
Vol 10
(1)
◽
pp. 243-250
◽
Keyword(s):