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• W2136809653 abstract "Abstract For any ring S we define and describe its characteristic ring, k(S) . It plays the rôle of the usual characteristic even in rings whose additive structure, ( S , +), is complicated. The ring k(S) is an invariant of ( S , +) and also reflects certain non-additive properties of S . If R is a left faithful ring without identity element, we show how to use k(R) to embed R in a ring R 1 with identity. This unital overring of R inherits many ring properties of R ; for instance, if R is artinian, noetherian, semiprime Goldie, regular, biregular or a V -ring, so too is R 1 . In the case of regularity (or generalizations thereof), R 1 satisfies a universal property with respect to the adjunction of an identity" @default.
• W2136809653 created "2016-06-24" @default.
• W2136809653 creator A5058033335 @default.
• W2136809653 creator A5062752718 @default.
• W2136809653 date "1989-12-01" @default.
• W2136809653 modified "2023-09-24" @default.
• W2136809653 title "The characteristic ring and the “best” way to adjoin a one" @default.
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• W2136809653 doi "https://doi.org/10.1017/s1446788700033218" @default.
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