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
The class group of integral domains
โ 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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๐ SIMILAR VOLUMES
This paper studies the class group of a graded integral domain R = โ R . We prove that if the extension R0 โ 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[ ]) โผ = Cl(A) โ HCl(K[
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 โ ฮฅ (Z 2p ) and ฮฅ (Z p ) ฮฅ (Z 2p ). We also present a precise description of t
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.