Geodesic
Serial piecewise domains
Algebra and discrete mathematics, no. 4 (2007), pp. 59-72.

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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.
Keywords: hereditary ring, semihereditary ring, serial ring, Noetherian diagonal, prime radical
Mots-clés : piecewise domain, prime quiver. 
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     author = {Nadiya Gubareni and Marina Khibina},
     title = {Serial piecewise domains},
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     year = {2007},
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     url = {http://geodesic.mathdoc.fr/item/ADM_2007_4_a5/}
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Nadiya Gubareni; Marina Khibina. Serial piecewise domains. Algebra and discrete mathematics, no. 4 (2007), pp. 59-72. http://geodesic.mathdoc.fr/item/ADM_2007_4_a5/