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Title: | Lattice definability of certain matrix rings |
Authors: | Korobkov, S. S. |
Issue Date: | 2017 |
Publisher: | PU TURPION LTD |
Abstract: | Let R = M-n(K) be the ring of square matrices of order n >= 2 over the ring K = Z/p(k)Z, where p is a prime number, k is an element of N. Let R' be an arbitrary associative ring. It is proved that the subring lattices of the rings R and R' are isomorphic if and only if the rings R and R' are themselves isomorphic. In other words, the lattice definability of the matrix ring M-n(K) in the class of all associative rings is proved. The lattice definability of a ring decomposable into a direct (ring) sum of matrix rings is also proved. The results obtained are important for the study of lattice isomorphisms of finite rings. |
Keywords: | LATTICE ISOMORPHISMS OF ASSOCIATIVE RINGS MATRIX RINGS GALOIS RINGS |
URI: | http://elar.uspu.ru/handle/uspu/6686 |
DOI: | 10.1070/SM8654 |
Appears in Collections: | Научные публикации, проиндексированные в Scopus и Web of Science |
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