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http://hdl.handle.net/123456789/141
2022-09-25T08:10:04ZDiagonalizability theorems for matrices over rings with finite stable range
http://hdl.handle.net/123456789/153
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.
2005-01-01T00:00:00ZMaximality of affine group, and hidden graph cryptosystems
http://hdl.handle.net/123456789/152
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.
2005-01-01T00:00:00ZWreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups
http://hdl.handle.net/123456789/151
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.
2005-01-01T00:00:00ZOn the mean square of the Epstein zeta-function
http://hdl.handle.net/123456789/150
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