Rings all of whose additive group endomorphisms are left multiplications

International Journal of Mathematics and Mathematical Sciences

Michael I. Rosen¹  Ovedshisha² 

[1] Department of Mathematics, Brown University, Providence 02912, RI, USA;Department of Mathematics, University of Rhode Island, Kingston 02881, RI, USA;

关键词: ring;    group;    endomorphism;    ideal;    R-algebra;    valuation ring.;   

DOI  :  10.1155/S0161171284000314

来源: DOAJ

【 摘 要 】

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)≡ax. 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.

【 授权许可】

Unknown