On Goldie Extending Modules with Condition (C2) |
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Authors: | Isao Kikumasa |
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Institution: | Department of Mathematics, Faculty of Science, Yamaguchi University, Yoshida, Yamaguchi, Japan |
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Abstract: | A module M is said to be continuous if it is extending with the condition (C2) (cf. 6 Mohamed, S. H., Müller, B. J. (1999). Continuous and Discrete Modules. London Math. Soc. LNS, Vol. 147. Cambridge: Cambridge Univ. Press. Google Scholar]], 7 Oshiro, K. (1983). Continuous modules and quasi-continuous modules. Osaka J. Math. 20:681–694.Web of Science ®] , Google Scholar]]). In this article, we consider a 𝒢-extending module with (C2) which is a generalization of a continuous module. First, we show that any 𝒢-extending module with (C2) satisfies the exchange property. We also prove that, if M1 and M2 are 𝒢-extending modules with (C2), then M1 ⊕ M2 is 𝒢-extending with (C2) if and only if Mi is Mj-ejective (i ≠ j). |
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Keywords: | Continuous module Ejective module Goldie-extending module (Internal) Exchange property |
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