QUOTIENT GE-ALGEBRAS INDUCED BY F-PSEUDO-VALUATIONS

초록

This paper explores the construction of quotient GE-algebras induced by F-pseudo-valuations. We introduce a congruence relation defined by an F-pseudo-valuation and utilize it to construct the quotient GE-algebra. Key properties of this quotient structure, including its operations, identity elements, and adherence to GE-algebra axioms, are thoroughly examined. We establish several theorems that elucidate the interplay between the original GE-algebra and its quotient, focusing on the behavior of GE-filters and the properties of the canonical homomorphism. These findings enhance the understanding of how algebraic properties are preserved or transformed under quotienting in the context of GE-algebras. © 2026 Institute of Mathematics, University of Zielona Gora. All rights reserved.

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