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Title: Projections of Galois Rings
Authors: Korobkov, S. S.
Issue Date: 2015
Publisher: SPRINGER
Citation: Korobkov S. S. Projections of Galois Rings / S. S. Korobkov // Algebra and logic. — 2015. — Vol. 54, iss. 1. — P. 43030.
Abstract: Let R and R (phi) be associative rings with isomorphic subring lattices and phi be a lattice isomorphism (a projection) of the ring R onto the ring R (phi) . We call R (phi) the projective image of a ring R and call the ring R itself the projective preimage of a ring R (phi) . We study lattice isomorphisms of Galois rings. By a Galois ring we mean a ring GR(p (n) , m) isomorphic to the factor ring K[x]/(f(x)), where K = Z/p (n) Z, p is a prime, f(x) is a polynomial of degree m irreducible over K, and (f(x)) is a principal ideal generated by the polynomial f(x) in the ring K[x]. Properties of the lattice of subrings of a Galois ring depend on values of numbers n and m. A subring lattice L of GR(p (n) , m) has the simplest structure for m = 1 (L is a chain) and for n = 1 (L is distributive). It turned out that only in these cases there are examples of projections of Galois ring onto rings that are not Galois rings. We prove the following result (Thm. 4). Let R = GR(p (n) , q (m) ), where n > 1 and m > 1. Then R (phi) a parts per thousand... R.
DOI: 10.1007/s10469-015-9318-9
Appears in Collections:Научные публикации, проиндексированные в Scopus и Web of Science

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