Abstract:
In this work, the interaction between the fuzzy small-T-ABSO submodule, small prime submodule, and fuzzy socle are compared. We provide two new concepts fuzzy socle small prime submodule and fuzzy socle small T-ABSO submodule to address this question. The research uncovered a number of traits that supported the novel theories. Using simple algebraic methods, it is also discovered that fuzzy socle small T-ABSO and fuzzy socle T-ABSO have a link, for fuzzy direct sum and homomorphic images, in additione, we looked into the fuzzy socle smallT-ABSO submodule structure. The compatibility of fuzzy socle small T-ABSO submodule with other fuzzy submodule kinds is also discussed. The results of this study are crucial for defining a new fuzzy socle small TABSO.
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