Abstract. Recently an algebra based on proportional calculi was introdued by Tamilarasi and Mekalai in the year 2010 known as TM-algebras [3]. Kandaraj and Chandramouleeswaran [5] introduced the notion of derivation on d-algebras. In [6], we introduced the notion of derivations on TM-algebras. In this paper, we introduce the notion of t-derivation on TM-algebras. We study the properties of regular t-derivations on a TM-algebra and prove that the set of all t-derivations on a TM-algebra forms a semigroup under a suitable binary composition.

Received: December 26, 2012

AMS Subject Classification: 03G25, 06F35

Key Words and Phrases: BCK/BCI algebras, TM-algebras, derivations, t-derivations

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