Two-sided submodules and duo-modules

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Marta Maloid-Glebova

Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

December 13, 2016 at 15:05 in Lecture Room 377

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.

Marta Maloid-Glebova
December 13, 2016

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On semiscalar equivalence of lower order polynomial matrices

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Bogdan Shavarovskii

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

November 29, 2016 at 15:05 in Lecture Room 377

Abstract of talk

Let \mathbb{C} be the field of complex numbers and A(x),B(x) be n \times n matrices with the entries in the polynomial ring \mathbb{C}[x]. Then A(x) is said to be semiscalarly equivalent to B(x) if there exist matrices P in \mathrm{GL}(n,\mathbb{C}) and Q(x) in \mathrm{GL}(n,\mathbb{C}[x]) (i.e. \mathrm{det}Q(x) is a nonzero complex number) such that A(x)=PB(x)Q(x). 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 2 \times 2 and 3 \times 3 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.

Bogdan Shavarovskii
November 29, 2016

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Semiring analogue of dmp-ring

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Ivanna Melnyk

Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

November 15, 2016 at 15:05 in Lecture Room 377

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.

Ivanna Melnyk
November 15, 2016

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Semiscalar equivalence of polynomial matrices and matrix equations

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Vasyl’ Petrychkovych

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

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Nataliia Dzhaliuk

Department of Algebra, Pidstryhach
Institute for Applied Problems of
Mechanics and Mathematics of
NAS of Ukraine

November 1, 2016 at 15:05 in Lecture Room 377

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.

Vasyl’ Petrychkovych
Nataliia Dzhaliuk

November 1, 2016

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Dyadic range of ring

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Bohdan Zabavsky

Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

October 25, 2016 at 15:05 in Lecture Room 377

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.

Bohdan Zabavsky
October 25, 2016

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