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Algebra and Discrete Mathematics, 2007, выпуск 4, страницы 59–72
(Mi adm234)
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RESEARCH ARTICLE
Serial piecewise domains
Nadiya Gubarenia, Marina Khibinab a Institute of Econometrics & Computer Science, Technical University of Częestochowa, 42–200 Częestochowa, Poland
b Institute of Engineering Thermophysics, NAS, Kiev, Ukraine
Аннотация:
A ring $A$ is called a piecewise domain with respect to the complete set of idempotents $\{e_1, e_2,\ldots, e_m\}$ if every nonzero homomorphism $e_iA \rightarrow e_jA$ is a monomorphism. In this paper we study the rings for which conditions of being piecewise domain and being hereditary (or semihereditary) rings are equivalent. We prove that a serial right Noetherian ring is a piecewise domain if and only if it is right hereditary. And we prove that a serial ring with right Noetherian diagonal is a piecewise domain if and only if it is semihereditary.
Ключевые слова:
piecewise domain, hereditary ring, semihereditary ring, serial ring, Noetherian diagonal, prime radical, prime quiver.
Образец цитирования:
Nadiya Gubareni, Marina Khibina, “Serial piecewise domains”, Algebra Discrete Math., 2007, no. 4, 59–72
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm234 https://www.mathnet.ru/rus/adm/y2007/i4/p59
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