Abstract
In this work, we present the notion of a multiplier on AT-algebra and investigate several properties. Also, some theorems and examples are discussed. The notions of the kernel and the image of multipliers are defined. After that, some propositions related to isotone and regular multipliers are proved. Finally, the Left and the Right derivations of the multiplier are obtained
Highlights
Prabpayak and Leerawat introduced a new algebraic structure named KU-algebra. They studied a homomorphism of KU-algebra and discussed some ideals of this structure [1,2]
The notion of ATalgebra was introduced as a generalization of KU-algebra
Investigations on multipliers were published by various researchers in the context of rings and semigroups [4]
Summary
Prabpayak and Leerawat introduced a new algebraic structure named KU-algebra. They studied a homomorphism of KU-algebra and discussed some ideals of this structure [1,2]. Definition 3.1.Let ( ,∗ ,0) be anAT-algebra. Example 3.2.Let = *0, , , , + be a set with the operation , defined by the following table: Based on definition 2.1,( ,∗ ,0)is anAT-algebra and the self map of is defined by:
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