A class of finite rings
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R. Raghavendran (1970)
Compositio Mathematica
von Haeseler, Fritz, Petersen, A. (1998)
Beiträge zur Algebra und Geometrie
Krishnan Selvakumar, Manoharan Subajini (2016)
Czechoslovak Mathematical Journal
Let be a commutative ring with nonzero identity and the Jacobson radical of . The Jacobson graph of , denoted by , is defined as the graph with vertex set such that two distinct vertices and are adjacent if and only if is not a unit of . The genus of a simple graph is the smallest nonnegative integer such that can be embedded into an orientable surface . In this paper, we investigate the genus number of the compact Riemann surface in which can be embedded and explicitly...
Alkhamees, Yousif (1994)
International Journal of Mathematics and Mathematical Sciences
Cazaran, J., Kelarev, A.V. (1999)
Acta Mathematica Universitatis Comenianae. New Series
Petra Konečná (2006)
Czechoslovak Mathematical Journal
Let be a finite commutative ring with unity. We determine the set of all possible cycle lengths in the ring of polynomials with rational integral coefficients.
Michel Planat, Saniga, Metod, Kibler, Maurice R. (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Yangjiang Wei, Jizhu Nan, Gaohua Tang (2012)
Czechoslovak Mathematical Journal
Let be the ring of Gaussian integers modulo . We construct for a cubic mapping graph whose vertex set is all the elements of and for which there is a directed edge from to if . This article investigates in detail the structure of . We give suffcient and necessary conditions for the existence of cycles with length . The number of -cycles in is obtained and we also examine when a vertex lies on a -cycle of , where is induced by all the units of while is induced by all the...
Yangjiang Wei, Jizhu Nan, Gaohua Tang (2011)
Czechoslovak Mathematical Journal
The article studies the cubic mapping graph of , the ring of Gaussian integers modulo . For each positive integer , the number of fixed points and the in-degree of the elements and in are found. Moreover, complete characterizations in terms of are given in which is semiregular, where is induced by all the zero-divisors of .
Jizhu Nan, Yangjiang Wei, Gaohua Tang (2014)
Czechoslovak Mathematical Journal
For a finite commutative ring and a positive integer , we construct an iteration digraph whose vertex set is and for which there is a directed edge from to if . Let , where and is a finite commutative local ring for . Let be a subset of (it is possible that is the empty set ). We define the fundamental constituents of induced by the vertices which are of the form if , otherwise where U denotes the unit group of and D denotes the zero-divisor set of . We investigate...
Melvin Hochster, Craig Huneke (1989)
Mémoires de la Société Mathématique de France
Chikunji, Chiteng'a John (2005)
International Journal of Mathematics and Mathematical Sciences
В.А. Ратинов (1984)
Matematiceskij sbornik
В.Л. Куракин, V. L. Kurakin, V. L. Kurakin, V. L. Kurakin (1997)
Algebra i Logika
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