Homoflatness on Ideal Extensions |
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Authors: | Akbar Golchin |
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Institution: | (1) Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran |
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Abstract: | We consider monoids $S=G\dot{\cup} I$ where $G$ is a group and $I$ is an ideal of $S$ and show that if an $S$-act is principally
weakly homoflat or weakly homoflat as an $I^1$-act, then it has
these properties as an $S$-act. We also show that an $S$-act which
is (weakly) pullback flat, equalizer flat, (principally) weakly
kernel flat, translation kernel flat or satisfies Condition $(E)$
as an $I^1$-act may not generally have these properties as an
$S$-act. The flatness notions considered in this paper were
introduced in {\it V. Laan, Pullbacks and flatness properties of
acts I, Comm. Alg. ${\bf 29}(2)$ (2001), 829--850}. |
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Keywords: | |
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