derivations, equational logic and interpolation (extended abstract) Gerard R. Renardel de Lavalette Department of Mathematics and Computing Science University of Groningen, the Netherlands Abstract. We define abstract derivations for equational logic and use them to prove the interpolation property. We define abstract derivations for equational logic and use them to prove the interpolation prop...

In this paper, the notions of left-right (resp. right-left) t-derivations of BCC-algebras are studied and some properties on t-derivations of BCC-algebras are investigated. This paper also considers t-regular t -derivations and the dt-invariant on ideals of BCC-algebras. Mathematics Subject Classification: 06F35

‎Let $L$ be a Lie algebra‎, ‎$mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$‎. ‎We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields‎. ‎Also‎, ‎we classi...

using fixed pointmethods, we investigate approximately higher ternary jordan derivations in banach ternaty algebras via the cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$

2. Derivatives 10 2.1. Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2. Hasse-Schmidt derivatives ∂ z . . . . . . . . . . . . . . . . . . . . . 11 2.3. Hasse-Schmidt derivations in general . . . . . . . . . . . . . . . . . 18 2.4. Hasse-Schmidt derivations from A to B as algebra maps A→ B [[t]] 22 2.5. Extending Hasse-Schmidt derivations to localizations . ....