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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN In this article we consider the structure of finitely generated modules over right hereditary semiperfect semidistributive rings. We show in what way a description of finitely generated modules over these rings of bounded representation type can be reduced to a mixed matrix problem. Some special mix[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN The generalized model of asynchronous iterations and its application for implementation of the algebraic iterative algorithm ART on a non-synchronous computer structure is presented. The sufficient conditions for convergence of this algorithm are considered.
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN In this article we consider non-commutative valuation and discrete valuation rings. We give equivalent conditions for a ring to be a valuation and a discrete valuation ring.
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN The full structure of right hereditary semiperfect semidistributive rings of bounded representation type are given. This structure is given in terms of special graphs which can be considered as some generalization of Coxeter-Dynkin diagrams.
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Journal of Applied Mathematics and Computational Mechanics
EN In this paper we present some results for FDI-rings, i.e. rings with a complete set of pairwise orthogonal primitive idempotents. We consider the nilpotency index of ideals and give its upper band for ideals in some classes of rings. We also give a new proof of a criterion of semiprime FDI-rings to [...]
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Journal of Applied Mathematics and Computational Mechanics
EN This article presents some results about several district valuation rings with a common skew field of fractions. They are obtained from the approximation theorem for discrete valuation rings. These results give the possibility to solve basic mixed matrix problems for such rings. We present the solut[...]
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Journal of Applied Mathematics and Computational Mechanics
EN In this paper we consider O-species and their representations. These O-species are a type of a generalization of a species introduced by Gabriel. We also consider the tensor algebras of such O-species. It is proved that the category of all representations of an O-species and the category of all righ[...]
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Journal of Applied Mathematics and Computational Mechanics
EN The problem of describing representations of (D,O)-species is reduced to flat mixed matrix problems over discrete valuation rings and their common skew field of fractions.
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Journal of Applied Mathematics and Computational Mechanics
EN We describe weak (D,O)-species of bounded representation type in terms of Dynkin diagrams and diagrams with weights. We reduce the problem of their description to flat mixed matrix problems over discrete valuation rings and their common skew field of fractions.
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN The structure of right hereditary semiperfect semidistributive rings of bounded representation type is described in terms of Dynkin diagrams and diagrams with weights. We describe it using a reduction to mixed matrix problems.
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN In this paper right hereditary semiperfect semidistributive rings A = A(S,O) of bounded representation type are described in terms of Dynkin diagrams and diagrams with weights. We describe these rings using a reduction to mixed matrix problems over a discrete valuation ring and its skew field of fra[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN In this article we consider special classes of rings related to finite partially ordered sets over division rings and prime hereditary Noetherian rings. The structure and main properties of these rings are studied. These rings are closely connected with right hereditary SPSD-rings.
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Journal of Theoretical and Applied Computer Science
EN In this paper the additive algorithm of spectral analysis is considered. This algorithm consists of algebraic summation of samples of basis functions taken at certain points of an interval of an independent variable of a given function. Two variants of simulation of the additive algorithm are consid[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN The image reconstruction problem from projection data for some particular schemes of reconstruction is considered. There are used the Algebraic Reconstruction Technique (ART) and the chaotic algebraic iterative algorithm CHART to reconstruct high-construct objects from incomplete data. The influence[...]
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