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C-domains are defined via class semigroups, and every C- domain is a Mori domain with nonzero conductor whose complete integral closure is a Krull domain with finite class group. In order to extend the concept of C-domains to rings with zero divisors, we study v-Marot rings as generalizations of ordinary Marot rings and investigate their theory of regular divisorial ideals. Based on this we establish a generalization of a result well-known for integral domains. Let R be a v-Marot Mori ring, R＾ its complete integral closure, and suppose that the conductor f = (R : R＾) is regular. If the residue class ring R/f and the class group C(R＾) are both finite, then R is a C-ring. Moreover, we study both v-Marot rings and C-rings under various ring extensions.
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참고문헌 (28)
참고문헌 신청
A. Foroutan / 2005 / Monotone chains of factorizations in C-monoids, Arithmetical properties of commutative rings and monoids / Lect. Notes Pure Appl. Math. 241 : 99 ~ 113
A. Foroutan / 2006 / Factorization of powers in C-monoids / J. Algebra 304 (2) : 755 ~ 781
A. Geroldinger / 2006 / Non-Unique Factorizations, Algebraic, Combina-torial and Analytic Theory, Pure and Applied Mathematics, vol. 278 / Chapman &Hall/CRC
A. Geroldinger / 2009 / Additive group theory and non-unique factorizations, Combinatorial number theory and additive group theory / Birkhuser Verlag : 1 ~ 86
B. G. Kang / 1991 / A characterizations of Krull rings with zero divisors / J. Pure Appl. Algebra 72 (1) : 33 ~ 38
A. Foroutan / 2006 / Factorization of powers in C-monoids / J. Algebra 304 (2) : 755 ~ 781
A. Geroldinger / 2006 / Non-Unique Factorizations, Algebraic, Combina-torial and Analytic Theory, Pure and Applied Mathematics, vol. 278 / Chapman &Hall/CRC
A. Geroldinger / 2009 / Additive group theory and non-unique factorizations, Combinatorial number theory and additive group theory / Birkhuser Verlag : 1 ~ 86
B. G. Kang / 1991 / A characterizations of Krull rings with zero divisors / J. Pure Appl. Algebra 72 (1) : 33 ~ 38
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