In this paper we review the concepts of the superalgebra, superderivation and some properties of them. We will define algebraic and differential superderivations on a superalgebra and will prove some theorems about them, Then we consider a superalgebra bundle, that is an algebra bundle which its fibers are superalgebras and then characterize the superderivations of the algebra of sections of th...

In the paper, we extend the definition of generalized derivations to superalgebras and prove that a generalized superderivation g on a prime superalgebra A is represented as g(x) = ax + d(x) for all x ∈ A, where a is an element of Qmr (the maximal right ring of quotients of A) and d is a superderivation on A. Using the result we study two generalized superderivations when their product is also ...

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, 35195-363, Iran 3Young Researchers and Elite Club, Malayer Branch, Azad University, Malayer, Iran Full list of author information is available at the end of the article Abstract In this paper, we introduce the concept of normed Lie superalgebr...

We provide an elementary introduction to the (characteristic zero) theory of Letterplace Superalgebras, regarded as bimodules with respect to the superderivation actions of a pair of general linear Lie superalgebras, and discuss some applications.

Considering the problem of autonomous development of quantum mechanics in the broader context of solution of Hilbert's sixth problem (which relates to joint axiomatization of physics and probability theory), a formalism is evolved in this two-part work which facilitates the desired autonomous development and satisfactory treatments of quantum-classical correspondence and quantum measurements. T...

let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...