This is a special issue of the journal devoted to the jubilee of the outstanding Ukrainian mathematician, one of the founder of our journal Professor Yuriy Drozd. http://hdl.handle.net/123456789/140 2026-04-15T21:31:14Z 2026-04-15T21:31:14Z Zabavsky, Bogdan http://hdl.handle.net/123456789/153 2020-01-24T21:28:48Z 2005-01-01T00:00:00Z

Diagonalizability theorems for matrices over rings with finite stable range Zabavsky, Bogdan We construct the theory of diagonalizability for matrices over Bezout ring with finite stable range. It is shown that every commutative Bezout ring with compact minimal prime spec- trum is Hermite. It is also shown that a principal ideal domain with stable range 1 is Euclidean domain, and every semilocal principal ideal domain is Euclidean domain. It is proved that every matrix over an elementary divisor ring can be reduced to "almost" diagonal matrix by elementary transformations.

2005-01-01T00:00:00Z Ustimenko, Vasiliy A. http://hdl.handle.net/123456789/152 2020-01-24T21:28:37Z 2005-01-01T00:00:00Z

Maximality of affine group, and hidden graph cryptosystems Ustimenko, Vasiliy A. We describe a new algebraic-combinatorial method of public key encryption with a certain similarity to the well known Imai-Matsumoto. We use the general idea to treat vertices of a linguistic graph (see [21] and further references) as messages and use the iterative process to walk on such graph as encryption process. To hide such encryption (graph and walk on it) we will use two affine transformation. Like in Imai Matsumoto encryption the public rule is just a direct polynomial map from the plaintext to the ciphertext. The knowledge about graph and chosen walk on them (the key) allow to decrypt a ciphertext fast. We hope that the system is secure even in the case when the graph is Public but the walk is hidden. In case of "public" graph we can use same encryption as private key algorithm with the resistance to attacks when adversary knows several pairs:(plaintext, ciphertext). We shall discuss the general idea of combining affine transformations and chosen polynomial map of deg 2 in case of prime field Fp. As it follows from the maximality of affine group each bijection on Fp n can be obtained by such combining.

2005-01-01T00:00:00Z Sushchansky, Vitaly I. Netreba, Nataliya V. http://hdl.handle.net/123456789/151 2020-01-24T21:28:10Z 2005-01-01T00:00:00Z

Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups Sushchansky, Vitaly I.; Netreba, Nataliya V. We define a wreath product of a Lie algebra L with the one-dimensional Lie algebra L1 over Fp and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of finite symmetric group Spm is isomorphic to the wreath product of m copies of L1. As a corollary we describe the Lie algebra associated with Sylow p-subgroup of any symmetric group in terms of wreath product of one-dimensional Lie algebras.

2005-01-01T00:00:00Z Savastru, O. V. Varbanets, P. D. http://hdl.handle.net/123456789/150 2020-01-24T21:28:39Z 2005-01-01T00:00:00Z

On the mean square of the Epstein zeta-function Savastru, O. V.; Varbanets, P. D. We consider the second power moment of the Epstein zeta-function and construct the asymptotic formula in special case, when '0(u, v) = u2 + Av2, A > 0, A 1, 2(mod 4) and '0(u, v) belongs to the one-class kind G0 of the quadratic forms ofdiscriminant −4A

2005-01-01T00:00:00Z