Alternative algebras admitting derivations with invertible values and invertible derivations

$(odot, oplus)$-Derivations and $(ominus, odot)$-Derivations on $MV$-algebras

In this paper, we introduce the notions of $(odot, oplus)$-derivations and $(ominus, odot)$-derivations for $MV$-algebras and discuss some related results. We study the connection between these derivations on an $MV$-algebra $A$ and the derivations on its boolean center. We characterize the isotone $(odot, oplus)$-derivations and prove that $(ominus, odot)$-derivations are isotone. Finally we d...

f-DERIVATIONS AND (f; g)-DERIVATIONS OF MV -ALGEBRAS

Recently, the algebraic theory of MV -algebras is intensively studied. In this paper, we extend the concept of derivation of $MV$-algebras and we give someillustrative examples. Moreover, as a generalization of derivations of $MV$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $MV$-algebras.Also, we investigate some properties of them.

Azumaya algebras and derivations

Derivations and skew derivations of the Grassmann algebras

Surprisingly, skew derivations rather than ordinary derivations are more basic (important) object in study of the Grassmann algebras. Let Λn = K⌊x1, . . . , xn⌋ be the Grassmann algebra over a commutative ring K with 12 ∈ K, and δ be a skew K-derivation of Λn. It is proved that δ is a unique sum δ = δ ev + δ of an even and odd skew derivation. Explicit formulae are given for δ and δ via the ele...

Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras