This article is cited in 5 scientific papers (total in 5 papers)
Integrally closed rings
A. A. Tuganbaev
This paper studies integrally closed rings. It is shown that a semiprime integrally closed Goldie ring is the direct product of a semisimple Artinian ring and a finite number of integrally closed invariant domains that are classically integrally closed in their (division) rings of fractions. It is shown also that an integrally closed ring has a classical ring of fractions and is classically integrally closed in it.
Next, integrally closed Noetherian rings are considered. It is shown that an integrally closed Noetherian ring all of whose nonzero prime ideals are maximal is either a quasi-Frobenius ring or a hereditary invariant domain.
Finally, those Noetherian rings all of whose factor rings are invariant are described, and the connection between integrally closed rings and distributive rings is examined.
Bibliography: 13 titles.
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Mathematics of the USSR-Sbornik, 1982, 43:4, 485–498
MSC: Primary 16A08, 16A14, 16A30, 16A33, 16A34, 16A52; Secondary 13B20
A. A. Tuganbaev, “Integrally closed rings”, Mat. Sb. (N.S.), 115(157):4(8) (1981), 544–559; Math. USSR-Sb., 43:4 (1982), 485–498
Citation in format AMSBIB
\paper Integrally closed rings
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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A. A. Tuganbaev, “Plane modules and distributivity”, Russian Math. Surveys, 50:6 (1995), 1314–1315
A. A. Tuganbaev, “Distributively decomposable rings”, Russian Math. Surveys, 51:3 (1996), 569–570
A. A. Tuganbaev, “Avtomorfizm-prodolzhaemye i endomorfizm-prodolzhaemye moduli”, Fundament. i prikl. matem., 21:4 (2016), 175–248
A. N. Abyzov, Ch. K. Kuin, A. A. Tuganbaev, “Moduli, invariantnye otnositelno avtomorfizmov i idempotentnykh endomorfizmov svoikh obolochek i nakrytii”, Algebra, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 159, VINITI RAN, M., 2019, 3–45
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