THE u-S-GLOBAL DIMENSIONS OF COMMUTATIVE RINGS
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Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. First, we introduce and study the $u$-$S$-projective dimension and $u$-$S$-injective dimension of an $R$-module, and then explore the $u$-$S$-global dimension $u$-$S$-\gld$(R)$ of a commutative ring $R$, i.e., the supremum of $u$-$S$-projective dimensions of all $R$-modules. Finally, we investigate $u$-$S$-global dimensions of factor rings and polynomial rings.
Abstract
Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. First, we introduce and study the $u$-$S$-projective dimension and $u$-$S$-injective dimension of an $R$-module, and then explore the $u$-$S$-global dimension $u$-$S$-\gld$(R)$ of a commutative ring $R$, i.e., the supremum of $u$-$S$-projective dimensions of all $R$-modules. Finally, we investigate $u$-$S$-global dimensions of factor rings and polynomial rings.
참고문헌 (7)
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