01.01.06 (Mathematical logic, algebra, and number theory)
Birth date:
11.09.1961
E-mail:
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Keywords:
soluble groups and generalisations; groups of finite rank; group rings and generalisations; primitivity of group rings; representations of groups an group algebras; primitive representations.
Subject:
We considered ideals in group rings of abelian and nilpotent groups with operators. Due to obtained results, we developed new techniques and approaches which allow to find subgroups from which representations of soluble groups of finite rank are induced. This allowed us to prove that in the class of metabelian groups of finite rank only polycyclic groups may have primitive irreducible representation over a finitely generated field of characteristic zero. Besides, we proved the Nullstellenzats for group algebras of metabelian groups of finite rank and obtained a criterion for primitivity of these algebras.
Biography
Graduated from Faculty of Mathematics and Mechanics of Dnepropetrovsk State University (DSU) in 1984 (department of geometry and algebra). Ph.D. thesis was defended in 1988. My list of publications contains 24 papers published in reviewed editions.
Since 1995 I am a member of the American Mathematical Society.
Main publications:
Tushev A. V. Spectra of conjugated ideals in group algebras of abelian groups of finite rank and control theorems. // Glasgow Math. J., 1996, 38, 309–320.
Tushev A. V. On modules over group rings of soluble groups of finite rank. // London Math. Soc. Lecture Notes Series, 1999, 261, 718–727.
Tushev A. V. Induced modules over group algebras of metabelian groups of finite rank. // Comm. Algebra, 1999, 27(12), 5921–5938.
A. V. Tushev, “On the controllers of prime ideals of group algebras of Abelian torsion-free groups of finite rank over a field of positive
characteristic”, Mat. Sb., 197:9 (2006), 115–160; Sb. Math., 197:9 (2006), 1365–1404
A. V. Tushev, “On the primitivity of group algebras of certain classes of soluble groups of finite rank”, Mat. Sb., 186:3 (1995), 143–160; Sb. Math., 186:3 (1995), 447–463
A. V. Tushev, “On soluble groups with finite homomorphic images of bounded rank”, Mat. Zametki, 56:5 (1994), 136–139; Math. Notes, 56:5 (1994), 1190–1192
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