On the quasikronecker product of Gorenstein matrices (in Ukrainian)

M.V.Plakhotnyk

The construction of quasikronecker product of matrices is introduced in this article. It preserves the matrix property of being Gorenstein matrix and defines the semigroup structure on the set of Gorenstein matrices. Also the cyclic index of direct product of permutations is expressed in terms of cyclic indices of the initial ones. This is used to show impossibility of using quasikronecker product for describing all Gorenstein matrices.

1. Кириченко В.В. Квазифробениусовы кольца и горенштейновы порядки// Труды мат. института им. Стеклова. -- 1978. -- T.148. -- C.168--178.

2. Chernousova Zh.T., Dokuchaev M.A., Khibina M.A., Kirichenko V.V., Miroshnichenko S.G., Zhuravlev~N.V. Tiled orders over diskrete valuation rings, finite Markov chains and partially orded sets// São Paulo, Brasil, 2004 (preprint).

3. Журавльов В.М., Черноусова Ж.Т. Циклічні горенштейнові порядки з малим числом вершин// Вісн. Київ. ун-ту. Cер. фіз.-мат. -- 2002. -- №2. -- С.33--40.

4. Dokuchaev M.A., Kirichenko V.V., Zelensky A.V., Zhuravlev V.N. Gorenstein matrices// Algebra and diskrete mathematics. -- 2005. -- №1. -- P.8--29.

5. Plakhotnyk M. On the dimension of the space of Gorenstein matrices for some types of correspond permutations// 5th Iinternational Algebraic Conference in Ukraine. -- P.157.

6. Weichsel P.M. The Kronecker product of graphs// Proc. Amer. Math. Soc. -- 1962. -- V.13,№1. -- P.47--52.

7. McAndrew M.H. On the product of directed graphs// Proc. Amer. Math. Soc. -- 1963. -- V.14,№4. -- P.600--606.

8. Сущанський В.І, Сікора В.С. Операції на підстановках. Теорія та застосування. -- Чернівці: Рута, 2003. -- 256 с.

	On the quasikronecker product of Gorenstein matrices (in Ukrainian)
Author	M.V.Plakhotnyk Shevchenko Kyiv National University
Abstract	The construction of quasikronecker product of matrices is introduced in this article. It preserves the matrix property of being Gorenstein matrix and defines the semigroup structure on the set of Gorenstein matrices. Also the cyclic index of direct product of permutations is expressed in terms of cyclic indices of the initial ones. This is used to show impossibility of using quasikronecker product for describing all Gorenstein matrices.
Keywords	quasikronecker product, Gorenstein matrix, semigroup, cyclic index
DOI	doi:10.30970/ms.28.1.3-10
Reference	1. Кириченко В.В. Квазифробениусовы кольца и горенштейновы порядки// Труды мат. института им. Стеклова. -- 1978. -- T.148. -- C.168--178. 2. Chernousova Zh.T., Dokuchaev M.A., Khibina M.A., Kirichenko V.V., Miroshnichenko S.G., Zhuravlev~N.V. Tiled orders over diskrete valuation rings, finite Markov chains and partially orded sets// São Paulo, Brasil, 2004 (preprint). 3. Журавльов В.М., Черноусова Ж.Т. Циклічні горенштейнові порядки з малим числом вершин// Вісн. Київ. ун-ту. Cер. фіз.-мат. -- 2002. -- №2. -- С.33--40. 4. Dokuchaev M.A., Kirichenko V.V., Zelensky A.V., Zhuravlev V.N. Gorenstein matrices// Algebra and diskrete mathematics. -- 2005. -- №1. -- P.8--29. 5. Plakhotnyk M. On the dimension of the space of Gorenstein matrices for some types of correspond permutations// 5th Iinternational Algebraic Conference in Ukraine. -- P.157. 6. Weichsel P.M. The Kronecker product of graphs// Proc. Amer. Math. Soc. -- 1962. -- V.13,№1. -- P.47--52. 7. McAndrew M.H. On the product of directed graphs// Proc. Amer. Math. Soc. -- 1963. -- V.14,№4. -- P.600--606. 8. Сущанський В.І, Сікора В.С. Операції на підстановках. Теорія та застосування. -- Чернівці: Рута, 2003. -- 256 с.
Pages	3-10
Volume	28
Issue	1
Year	2007
Journal	Matematychni Studii
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