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Abstract

This research analyses the correlation that exists between fuzzy T-ABSO and fuzzy socle. To answerthis question, we define a new concept called, fuzzy socle T-ABSO submodules. Results showed many propertiesthat satisfied the new notion. In addition, we applied some algebra operations and found the relationship betweenfuzzy T-ABSO and fuzzy socle -T-ABSO. We also investigated the structure of fuzzy socle T-ABSO sub- modules ofa module under fuzzy direct sum, homomorphic image and intersection. Moreover, the relation between fuzzy socleT-ABSO sub-module and other types of fuzzy sub-module was presented. The implications of this study could beused to define new concepts that depend on fuzzy socle T-ABSO concepts.

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