Rings all of whose additive group endomorphisms are left multiplications

Michael I. Rosen and Oved Shisha

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-5

Abstract:

Motivated by Cauchy's functional equation f ( x + y ) = f ( x ) + f ( y ) , we study in § 1 special rings, namely, rings for which every endomorphism f of their additive group is of the form f ( x ) ≡ a x . In § 2 we generalize to R algebras ( R a fixed commutative ring) and give a classification theorem when R is a complete discrete valuation ring. This result has an interesting consequence, Proposition 12 , for the theory of special rings.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:698757

DOI: 10.1155/S0161171284000314

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