
StatusThe thesis was presented on the 17 May, 2016Approved by NCAA on the 5 July, 2016 Abstract– 0.27 Mb / in romanianThesisCZU 512.556.3
1.45 Mb /
in russian 
Thesis structure: the thesis is written in Russian and consists of an introduction, three
chapters, general conclusions and recommendations, bibliography of 85 titles, 127 pages of main
text. The obtained results are published in 15 scientific papers.
Field of study of the thesis: belongs to study of properties of homomorphisms and isomorphisms
of pseudonormed rings and their applications.
Thesis aim and objectives:
– determination of classes of special isomorphisms of pseudonormed rings for which
analogues of the second isomorphism theorem hold;
– study of properties of special isomorphisms of pseudonormed rings;
– study of constructions of pseudonormed rings which are preserving special isomorphisms.
Scientific novelty and originality:
– were definited concepts of a semiisometric isomorphism (semiisometric isomorphism
on the left, semiisometric isomorphism on the right) of pseudonormed rings;
– were proved criterions of a semiisometric isomorphism (semiisometric isomorphism
on the left, semiisometric isomorphism on the right);
– were established some properties of a semiisometric isomorphism (semiisometric
isomorphism on the left, semiisometric isomorphism on the right);
– were proved theorems about preservation of a semiisometric isomorphism (semiisometric
isomorphism on the left, semiisometric isomorphism on the right) for some
constructions of pseudonormed rings.
The important scientific solved problem consists of determination of classes of special isomorphisms of pseudonormed rings for which analogues of the second isomorphism theorem hold and study of their properties which led to study of constructions of pseudonormed rings which are preserving these isomorphisms.
The theoretical significance and applicative value of the thesis consists in development of research methods for isomorphisms of pseudonormed rings on semiisometry (semiisometry on the left, semiisometry on the right), establishment of sufficient conditions of preservation of semiisometric isomorphism (semiisometric isomorphism on the left, semiisometric isomorphism on the right) for some constructions of pseudonormed rings.
The implementation of the scientific results:
– the results and methods which are developed in the thesis can be applied for further investigations
of isomorphisms and homomorphisms of pseudonormed rings and Banach rings;
– the results of the thesis can be applied to the construction of the general theory of radicals
of pseudonormed rings;
– the results of the thesis can serve as support for master thesis and can be used as
content for some special courses of undergraduate and graduate programs for students of
mathematical specialties.