WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 21, 2022
Cancellation On Fuzzy Projective Modules And Schanuel’s Lemma Using Its Conditioned Class
Authors: , ,
Abstract: As an extension, the current study looks at fuzzy projective module cancellation and fuzzy module
equivalence in specific situations. While addressing cancellation, we provide the necessary and sufficient
criteria for fuzzy projective modules to fulfill cancellation over the polynomial ring and ring R. Furthermore,
using fuzzy p-poor modules, we have established an intriguing result in Schanuel’s lemma, claiming that
for any two fuzzy exact sequences of fuzzy R-modules $$ 0 \rightarrow μ1\:\xrightarrow{\overline{f1}}\:η1\:\xrightarrow{\overline{g1}}\: μ \rightarrow 0$$ and $$ 0 \rightarrow μ2\:\xrightarrow{\overline{f2}}\:η2\:\xrightarrow{\overline{g2}}\: μ \rightarrow 0$$. If η1 and η2 are fuzzy p-poor modules then $$ μ1 ⊕ η2 \cong μ2 ⊕ η1$$. The same is reinforced by an acceptable
illustration of fuzzy p-poor module.
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Keywords: fuzzy modules, fuzzy projective module, fuzzy projective poor-module, fuzzy subprojective poor-module, schanuel’s lemma
Pages: 476-486
DOI: 10.37394/23206.2022.21.55