On t-derivations of PMS-algebras

Area of Science:

• Algebraic Structures
• Abstract Algebra
• Mathematical Logic

Background:

• PMS algebras represent a significant generalization of established algebraic structures like Boolean and MV-algebras.
• Recent research has focused on the extensive study of PMS algebras and their properties.

Purpose of the Study:

• To introduce and define the concept of t-derivations on PMS algebras.
• To investigate the fundamental properties of t-derivations and regular t-derivations within PMS algebras.
• To explore novel results concerning t-derivations, particularly on the G-part of PMS algebras.

Main Methods:

• Definition of t-derivations as specific mappings between PMS algebras.
• Characterization of properties for t-derivations and regular t-derivations.
• Investigation of t-derivations within the G-part of PMS algebras.
• Proof of the semigroup property for the set of all t-derivations.

Main Results:

• Established characterizations for t-derivations on PMS algebras.
• Presented novel findings regarding t-derivations on the G-part of PMS algebras.
• Proved that the set of all t-derivations on a PMS algebra constitutes a semigroup.

Conclusions:

• The paper offers a thorough examination of t-derivations in the context of PMS algebras.
• New results and detailed property characterizations of t-derivations have been established.
• The findings enhance the understanding of PMS algebras and their related algebraic structures.