On classification of low-dimensional Lie algebras
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Fedorchuk Vasyl’, Fedorchuk Volodymyr
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March 21, 2017 at 15:05 in Lecture Room 372 |
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Abstract of talk
We plan to present a short review of the results related to the classification of low-dimensional (
)
Lie algebras.
Fedorchuk Volodymyr
March 21, 2017
Commutative Bezout domains whose non-trivial finite homomorphic images are semipotent rings
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Bohdan Zabavsky, Sofia Bilavska-KudlataDepartment of Algebra and Logic |
March 7, 2017 at 15:05 in Lecture Room 377 |
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Abstract of talk
In this talk we will investigate the structure of commutative Bezout domain whose non-trivial finite homorphic images are semipotent rings.
Sofia Bilavska-Kudlata
March 7, 2017
Two-sided submodules and duo-modules
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Marta Maloid-GlebovaDepartment of Algebra and Logic |
December 13, 2016 at 15:05 in Lecture Room 377 |
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Abstract of talk
Talk will be devoted to duo-modules and their generalizations.
In particular, will be presented definition of two-sided submodule and will be studied its properties. Also will be given notions of duo-module, strongly duo-module, fully-ordered module and will be investigated their properties. In particular, will be given relationships between duo-modules and multiplication modules.
December 13, 2016
On semiscalar equivalence of lower order polynomial matrices
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Bogdan ShavarovskiiDepartment of Algebra, Pidstryhach |
November 29, 2016 at 15:05 in Lecture Room 377 |
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Abstract of talk
Let 
be the field of complex numbers and 
be 
matrices with the entries in the polynomial ring ![\mathbb{C}[x]](http://unial.in.ua/wp-content/ql-cache/quicklatex.com-d8595420a1973790f204cdaa0e350b66_l3.png "Rendered by QuickLaTeX.com")
. Then 
is said to be semiscalarly equivalent to 
if there exist matrices 
in 
and 
in ![\mathrm{GL}(n,\mathbb{C}[x])](http://unial.in.ua/wp-content/ql-cache/quicklatex.com-ee26e8a50428a2f3d714a9c36bba2858_l3.png "Rendered by QuickLaTeX.com")
(i.e. 
is a nonzero complex number) such that 
. The semiscalarity concept is itself interesting as it occurs naturally in the various problems in the applied mathematics and engineering. However, the problem of finding a complete set of (computable) semiscalarity equivalence invariants is very difficult. In this report we are going to discuss some classes of 
and 
polynomial matrices such that it is possible to obtain the complete invariants system for their elements, and the canonical forms for such matrices with respect to semiscalar equivalence are indicated as well.
November 29, 2016
Semiring analogue of dmp-ring
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Ivanna MelnykDepartment of Algebra and Logic |
November 15, 2016 at 15:05 in Lecture Room 377 |
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Abstract of talk
We will present some new examples and prove the properties of semiring differential ideals, as well as radical differential ideals of commutative differential semirings.
It will be shown that any radical differential subtractive ideal is an intersection of prime differential subtractive ideals. Finally, we characterize differential semirings in which the radical of every differential subtractive ideal is again differential.
November 15, 2016
Semiscalar equivalence of polynomial matrices and matrix equations
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Vasyl’ PetrychkovychDepartment of Algebra, Pidstryhach |
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Nataliia DzhaliukDepartment of Algebra, Pidstryhach |
November 1, 2016 at 15:05 in Lecture Room 377 |
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Abstract of talk
We will describe the solutions of the polynomial Diophantine matrix equations and
Sylvester matrix equations based on the standard form of polynomial matrices with respect to semiscalar equivalence.
Nataliia Dzhaliuk
November 1, 2016
Dyadic range of ring
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Bohdan ZabavskyDepartment of Algebra and Logic |
October 25, 2016 at 15:05 in Lecture Room 377 |
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Abstract of talk
It will be introduced the notion of dyadic range of ring and proved some its basic properties.
Main teorem. A commutative Bezout ring is an elementary divisor ring if and only if it is a ring of dyadic range 1.
October 25, 2016