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|Title:||Lattice definability of certain matrix rings|
|Authors:||Korobkov, S. S.|
|Citation:||Korobkov S. S. Lattice definability of certain matrix rings / S. S. Korobkov // Sbornik mathematics. — 2017. — Vol. 208, iss. 1. — P. 90-102.|
|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|
|Appears in Collections:||Научные публикации, проиндексированные в Scopus и Web of Science|
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