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The class group of integral domains

โœ Scribed by David F. Anderson; Gyu Whan Chang


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
192 KB
Volume
264
Category
Article
ISSN
0021-8693

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๐Ÿ“œ SIMILAR VOLUMES


Class semigroups of integral domains
โœ S. Kabbaj; A. Mimouni ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 210 KB

This paper seeks ring-theoretic conditions of an integral domain R that reflect in the Clifford property or Boolean property of its class semigroup S(R), that is, the semigroup of the isomorphy classes of the nonzero (integral) ideals of R with the operation induced by multiplication. Precisely, in

On the class group of a Mori domain
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On the class group of a graded domain
โœ S. El Baghdadi; L. Izelgue; S. Kabbaj ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 130 KB

This paper studies the class group of a graded integral domain R = โˆˆ R . We prove that if the extension R0 โŠ‚ R is inert, then Cl(R) = HCl(R) if and only if R is almost normal. As an application, we state a decomposition theorem for class groups of semigroup rings, namely, Cl(A[ ]) โˆผ = Cl(A) โŠ• HCl(K[

Elasticities of Krull domains with finit
โœ K. Kattchee ๐Ÿ“‚ Article ๐Ÿ“… 2004 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 230 KB

Fix any positive integer b, and consider the set ฮฅ (Z b ) of all values ฯ(R), where R is a Krull domain with divisor class group Z b , and ฯ(R) denotes the elasticity of R. We focus on the case b = 2p, showing that 2p-1 p โˆˆ ฮฅ (Z 2p ) and ฮฅ (Z p ) ฮฅ (Z 2p ). We also present a precise description of t

On the Solvability of a Class of Second
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j makes sense. If โ€ is bounded then, with the understanding that Z 0 [ ะป, ลฝ . ลฝ . A3 is trivially satisfied with s โ€, s ะป, and m s 0, and iii then imposes no restriction on the kernel k.