Rings all of whose additive group endomorphisms are left multiplications
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 com...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000314 |
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| _version_ | 1849685117512974336 |
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| author | Michael I. Rosen Oved shisha |
| author_facet | Michael I. Rosen Oved shisha |
| author_sort | Michael I. Rosen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c2b09a74bd80450dae9c266b91969457 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c2b09a74bd80450dae9c266b919694572025-08-20T03:23:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017229730110.1155/S0161171284000314Rings all of whose additive group endomorphisms are left multiplicationsMichael I. Rosen0Oved shisha1Department of Mathematics, Brown University, Providence 02912, RI, USADepartment of Mathematics, University of Rhode Island, Kingston 02881, RI, USAMotivated 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.http://dx.doi.org/10.1155/S0161171284000314ringgroupendomorphismidealR-algebravaluation ring. |
| spellingShingle | Michael I. Rosen Oved shisha Rings all of whose additive group endomorphisms are left multiplications International Journal of Mathematics and Mathematical Sciences ring group endomorphism ideal R-algebra valuation ring. |
| title | Rings all of whose additive group endomorphisms are left multiplications |
| title_full | Rings all of whose additive group endomorphisms are left multiplications |
| title_fullStr | Rings all of whose additive group endomorphisms are left multiplications |
| title_full_unstemmed | Rings all of whose additive group endomorphisms are left multiplications |
| title_short | Rings all of whose additive group endomorphisms are left multiplications |
| title_sort | rings all of whose additive group endomorphisms are left multiplications |
| topic | ring group endomorphism ideal R-algebra valuation ring. |
| url | http://dx.doi.org/10.1155/S0161171284000314 |
| work_keys_str_mv | AT michaelirosen ringsallofwhoseadditivegroupendomorphismsareleftmultiplications AT ovedshisha ringsallofwhoseadditivegroupendomorphismsareleftmultiplications |