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- W1990935265 abstract "Let R be any integral domain. The minimal (commutative unital) ring extensions S of R are, up to R -algebra isomorphism, of three nonoverlapping types: (i) the domains S that contain R and are minimal ring extensions of R ; (ii) the idealizations R ( + ) R / M arising from maximal ideals M of R ; and (iii) the direct products R × R / M arising from maximal ideals M of R . Distinct maximal ideals of R lead to nonisomorphic idealizations (respectively direct products) in case (ii) (respectively case (iii)). If R is not a field, then distinct domains S arising in case (i) within the same quotient field of R are not isomorphic as R -algebras. If R is a field K , then the domains S arising in (i) are the minimal (necessarily algebraic) field extensions of K ; in this case, distinct such fields S 1 , S 2 are K -algebra isomorphic if and only if S i = K ( α i ) where α 1 , α 2 are roots of the same irreducible polynomial in K [ X ] ." @default.
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- W1990935265 date "2006-11-01" @default.
- W1990935265 modified "2023-10-17" @default.
- W1990935265 title "A classification of the minimal ring extensions of an integral domain" @default.
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- W1990935265 doi "https://doi.org/10.1016/j.jalgebra.2005.10.005" @default.
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