منابع مشابه
Class Semigroups of Integral Domains
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 Section 3, we characterize integrally closed domains with Boolean class semigoup; in this case, S...
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The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by ideal tmultiplication. This paper investigates ring-theoretic properties of an integral domain that reflect reciprocally in the Clifford or Boolean property of its t-class semigroup. Contexts (including Lipman and Sally-Vasconcelos stability) that suit best t-multi...
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The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by t-multiplication. This paper investigates integral domains with Boolean t-class semigroup with an emphasis on the GCD and stability conditions. The main results establish t-analogues for well-known results on Prüfer domains and Bézout domains of finite character. M...
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Let A be an Ä-order in a semisimple finite dimensional /(-algebra, where K is an algebraic number field, and R is the ring of algebraic integers of K. Denote by C(A) the reduced class group of the category of locally free left A-lattices. Choose A= ZC, the integral group ring of a finite group G, and let A be a maximal Z-order in QG containing A. There is an epimorphism C(A)-C(A'), given by JIÍ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2003
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00139-x