Kulakovska I. Finite directed graphs and their applications to structural theory of rings

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0406U002586

Applicant for

Specialization

  • 01.01.06 - Алгебра і теорія чисел

14-06-2006

Specialized Academic Board

Д 26.001.18

Taras Shevchenko National University of Kyiv

Essay

In the dissertation we apply technique, connected with the notions of quiver of ring and tensor algebras of bimodule, to the study of right serial rings. It give a simple description of a class of rings that contains right serial algebras over a perfect field. Moreover, right serial quasi-Frobenius and right serial hereditary rings are described. We investigate connections be-tween an indecomposable reduced semiperfect right noetherian semiprime semidistributive rings and some rings of quivers associated with such ring. We describe bipartite graphs that appear under the study of finitely presented modules. We prove the theorem about semiprimary semidistributive rings of finite type with zero square of radical (diagrams of such rings contain the Dynkin schemes).

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