Abstract
Let \(R\) be a ring with center \(Z\). A map \(D\) of \(R\) (resp. \(T\) of \(R\)) is called a centrally-extended derivation (resp. a centrally-extended endomorphism) if for each \(x,y\in R, D(x+y)-D(x)-D(y)\in Z\) and \(D(xy)-D(x)y-xD(y)\in Z\) (resp. \(T(x+y)-T(x)-T(y)\in Z\) and \(T(xy)-T(x)T(y)\in Z\)). We discuss existence of such maps which are not derivations or endomorphisms, we study their effect on \(Z\), and we give some commutativity results.
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Bell, H.E., Daif, M.N. On centrally-extended maps on rings. Beitr Algebra Geom 57, 129–136 (2016). https://doi.org/10.1007/s13366-015-0244-8
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DOI: https://doi.org/10.1007/s13366-015-0244-8
Keywords
- Derivations
- Epimorphisms
- Centrally-extended derivations
- Centrally-extended epimorphisms
- Commutativity theorems