Weakly dual automorphism invariant and superfluous cotightness |
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| Authors: | Truong Cong Quynh M Tamer Koşan Tran Hoai Ngoc Nhan |
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| Institution: | 1. Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam;2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;3. truongcongquynh@tdtu.edu.vn;5. Department of Mathematics, Faculty of Sciences, Gazi University, Ankara, Turkey;6. Faculty of Basic Sciences, Vinh Long University of Technology Education, Vinh Long, Vietnam |
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| Abstract: | AbstractThe aim of the present paper is to introduce and study the dual concepts of weakly automorphism invariant modules and essential tightness. These notions are non-trivial generalizations of both weakly projectivity, dual automorphism invariant property and cotightness. We obtain certain relations between weakly projective modules, weakly dual automorphism invariant modules and superfluous cotight modules. It is proved that: (1) for right perfect rings, every module is a direct summand of a weakly dual automorphism invariant module and (2) weakly dual automorphism invariant modules are precisely superfluous cotight modules. |
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| Keywords: | Automorphism invariant module cotight module dual automorphism invariant module tight module weakly injective module weakly projective module |
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