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|Title:||Projections of Finite One-Generated Rings with Identity|
|Authors:||Korobkov, S. S.|
|Citation:||Korobkov S. S. Projections of Finite One-Generated Rings with Identity / S. S. Korobkov // Algebra and logic. — 2016. — Vol. 55, iss. 2. — P. 128-145.|
|Abstract:||Associative rings R and R' are said to be lattice-isomorphic if their subring lattices L(R) and L(R') are isomorphic. An isomorphism of the lattice L(R) onto the lattice L(R') is called a projection (or else a lattice isomorphism) of the ring R onto the ring R'. A ring R' is called the projective image of a ring R. Lattice isomorphisms of finite one-generated rings with identity are studied. We elucidate the general structure of finite one-generated rings with identity and also give necessary and sufficient conditions for a finite ring decomposable into a direct sum of Galois rings to be generated by one element. Conditions are found under which the projective image of a ring decomposable into a direct sum of finite fields is a one-generated ring. We look at lattice isomorphisms of one-generated rings decomposable into direct sums of Galois rings of different types. Three main types of Galois rings are distinguished: finite fields, rings generated by idempotents, and rings of the form GR(p(n),m), where m > 1 and n > 1. We specify sufficient conditions for the projective image of a one-generated ring decomposable into a sum of Galois rings and a nil ideal to be generated by one element.|
LATTICE ISOMORPHISMS OF ASSOCIATIVE RINGS
|Appears in Collections:||Научные публикации, проиндексированные в Scopus и Web of Science|
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