Generalized $(T, \Gamma, \Upsilon)$-Derivations on $c$-Subtraction Algebras

Chiranjibe Jana, Madhumangal Pal

Abstract

In a complicated subtraction ($c$-subtraction) algebra $X$, the notion of a new kind of derivation is introduced on $X$ called $(T,\Gamma,\Upsilon)$-derivation such that $F$ is monotone, as a generalization of derivation of $c$-subtraction and characterized some of its relevant properties. Some equivalent conditions provided on a $c$-subtraction algebra by the notion of isotone $(T,\Gamma,\Upsilon)$-derivation on $X$. By using the concept of isotone derivation,we study some interesting properties of it by the notion of $(T,\Gamma,\Upsilon)$-derivation when $F$ is monotone. Finally, generalized $(T,F)$-derivationon $c$-subtraction algebra is defined determined by a $T$-derivation $d_T$ and discussed.