Morita context and generalized (α, β)−derivations
| Autor: | Nadeem ur Rehman, Radwan Mohammed AL-Omary, Mohammed M. Al-Shomrani |
|---|---|
| Jazyk: | English<br />Portuguese |
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Boletim da Sociedade Paranaense de Matemática, Vol 31, Iss 1, Pp 153-166 (2013) |
| Druh dokumentu: | article |
| ISSN: | 0037-8712 2175-1188 |
| DOI: | 10.5269/bspm.v31i1.13682 |
| Popis: | Let $R$ and $S$ be rings of a semi-projective Morita context, and $\alpha, \beta$ be automorphisms of $R$. An additive mapping $F$: $R\to R$ is called a generalized $(\alpha,\beta)$-derivation on $R$ if there exists an $(\alpha,\beta)$-derivation $d$: $R\to R$ such that $F(xy)=F(x)\alpha(y)+\beta(x)d(y)$ holds for all $x,y \in R$. For any $x,y \in R$, set $[x, y]_{\alpha, \beta} = x \alpha(y) - \beta(y) x$ and $(x \circ y)_{\alpha, \beta} = x \alpha(y) + \beta(y) x$. In the present paper, we shall show that if the ring $S$ is reduced then it is a commutative, in a compatible way with the ring $R$ . Also, we obtain some results on bialgebras via Cauchy modules. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|