Some Homomorphism Properties of TM-Algebras

Abstract

Let X be a TM-algebra and I be an ideal of X. A homomorphism from X into another TM-algebra Y is a mapping h:X→ Y satisfying h(xy)=h(x)h(y) for all x,y ∈ X. In this research, we investigate some homomorphism properties in quotient TM-algebra X relative to the ideal I.

The First Isomorphism Theorem on QI-algebras

“…Afterwards, several structures of algebras such as BH-algebras [6], TM-algebras [7] and KU-algebras [12] were introduced and investigated. The fundamental concepts of abstract algebra such as ideals, congruences and homomorphisms were also studied on those algebraic structures (see [1], [11], [13]). Furthermore, many generalizations of BCK-algebras were introduced by several researchers.…”