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Quasi-isomorphism and some quasi-isomorphic invariants of QTAG-modules. (English) Zbl 1188.16002

Commun. Algebra 38, No. 2, 752-758 (2010); retraction note ibid. 45, No. 10, 4582 (2017).
Summary: For QTAG-modules the concept of quasi-isomorphism was defined by the authors [J. Rajasthan Acad. Phys. Sci. 5, No. 2, 153-158 (2006; Zbl 1114.16006)]. Two QTAG-modules are quasi-isomorphic when they contain cobounded submodules. Here we prove that cobounded submodules inherit basic submodules. Then we impose some restrictions on quasi-isomorphism and find that quasi-isomorphic modules with these restrictions are very different. We also study the quasi-isomorphism of direct sum of uniserial modules and some quasi-isomorphic variants. It is natural to ask if for two quasi-isomorphic QTAG-modules \(M,M'\) if \(M\) is a direct sum of countably generated uniserial modules, then \(M'\) is also the direct sum of countably generated uniserial modules or not. In the last section we obtain the condition under which this is possible.
Editorial remark: From the retraction note: “We, the Editors and Publishers of Communications in Algebra, have retracted this article. We are now cognisant of a substantially similar version of this article which was previously submitted to, and published in, the Pacific Journal of Mathematics.”

MSC:

16D80 Other classes of modules and ideals in associative algebras

Citations:

Zbl 1114.16006
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References:

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