On the structure of digraphs of polynomial transformations over finite commutative rings with unity
2018 ◽
Vol 28
(4)
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pp. 259-274
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Abstract The paper describes structural characteristics of the digraph of an arbitrary polynomial transformation of a finite commutative ring with unity. A classification of vertices of the digraph is proposed: cyclic elements, initial elements, and branch points are described. Quantitative results on such objects and heights of vertices are given. Besides, polynomial transformations are shown to have cycles whose lengths coincide with the lengths of cycles of the induced polynomial transformation over the field R/ℜ, where ℜ is the radical of the finite commutative local ring R.
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2019 ◽
Vol 19
(12)
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pp. 2050226
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2019 ◽
Vol 19
(09)
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pp. 2050173
2018 ◽
Vol 17
(07)
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pp. 1850121
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2012 ◽
Vol 11
(06)
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pp. 1250103
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2019 ◽
Vol 19
(02)
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pp. 2050039
2015 ◽
Vol 07
(01)
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pp. 1450064
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