Let R be a ring and S a class of R-modules. S-superfluous epimorphisms and S-essential monomorphisms are introduced and studied in this article. As applications, some new characterizations of von Neumann regular rings...Let R be a ring and S a class of R-modules. S-superfluous epimorphisms and S-essential monomorphisms are introduced and studied in this article. As applications, some new characterizations of von Neumann regular rings and perfect rings are given. Finally, these notions are also used to study minimal homomorphisms.展开更多
In this paper, we develop some operational calculus inspired from the Fredholm operator theory to investigate the S-essential spectra of the sum and the product of two operators acting on a Banach space. Furthermore, ...In this paper, we develop some operational calculus inspired from the Fredholm operator theory to investigate the S-essential spectra of the sum and the product of two operators acting on a Banach space. Furthermore, we apply the obtained results to determine the S-essential spectra of an integro-differential operator with abstract boundary conditions in L1（[-a,a]×[-1,1]）（a〉0）.展开更多
基金Supported by Specialized Research Fund for the Doctoral Program of Higher Education (20050284015)National Natural Science Foundation of China (10771096)
文摘Let R be a ring and S a class of R-modules. S-superfluous epimorphisms and S-essential monomorphisms are introduced and studied in this article. As applications, some new characterizations of von Neumann regular rings and perfect rings are given. Finally, these notions are also used to study minimal homomorphisms.
文摘In this paper, we develop some operational calculus inspired from the Fredholm operator theory to investigate the S-essential spectra of the sum and the product of two operators acting on a Banach space. Furthermore, we apply the obtained results to determine the S-essential spectra of an integro-differential operator with abstract boundary conditions in L1（[-a,a]×[-1,1]）（a〉0）.
