Rings over which all modules are I0-modules. II

All right R-modules are I0-modules if and only if either R is a right SV-ring or R/I(2) (R) is an Artinian serial ring such that the square of the Jacobson radical of R/I(2) (R) is equal to zero. © 2009 Springer Science+Business Media, Inc

Homomorphisms close to regular and their applications

This paper contains new and known results on homomorphisms that are close to regular. The main results are presented with proofs. © 2012 Springer Science+Business Media, Inc

Modules in Which Sums or Intersections of Two Direct Summands Are Direct Summands

© 2015 Springer Science+Business Media New York This paper contains new characterizations of SSPm. odules, SIP-modules, D3-modules, and C3-modules. These characterizations are used for the proof of new and known results related to SSP-modules and SIP-modules. We also apply obtained results to endo-regular modules

Retractable and Coretractable Modules

© 2016, Springer Science+Business Media New York.In this paper, we study mod-retractable modules, CSL-modules, fully Kasch modules, and their interrelations. Right fully Kasch rings are described. It is proved that for a module M of finite length, the following conditions are equivalent. (1) In the category σ(M), every module is retractable. (2) In the category σ(M), every module is coretractable. (3) M is a CSL-module. (4) ExtR1 (S1, S2) = 0 for any two simple nonisomorphic modules S1, S2 ∈ σ(M). (5) M is a fully Kasch module

Retractable and Coretractable Modules

© 2016, Springer Science+Business Media New York.In this paper, we study mod-retractable modules, CSL-modules, fully Kasch modules, and their interrelations. Right fully Kasch rings are described. It is proved that for a module M of finite length, the following conditions are equivalent. (1) In the category σ(M), every module is retractable. (2) In the category σ(M), every module is coretractable. (3) M is a CSL-module. (4) ExtR1 (S1, S2) = 0 for any two simple nonisomorphic modules S1, S2 ∈ σ(M). (5) M is a fully Kasch module

Retractable and Coretractable Modules

© 2016, Springer Science+Business Media New York.In this paper, we study mod-retractable modules, CSL-modules, fully Kasch modules, and their interrelations. Right fully Kasch rings are described. It is proved that for a module M of finite length, the following conditions are equivalent. (1) In the category σ(M), every module is retractable. (2) In the category σ(M), every module is coretractable. (3) M is a CSL-module. (4) ExtR1 (S1, S2) = 0 for any two simple nonisomorphic modules S1, S2 ∈ σ(M). (5) M is a fully Kasch module

Rings over which all modules are I0-modules. II

All right R-modules are I0-modules if and only if either R is a right SV-ring or R/I(2) (R) is an Artinian serial ring such that the square of the Jacobson radical of R/I(2) (R) is equal to zero. © 2009 Springer Science+Business Media, Inc

Homomorphisms close to regular and their applications

This paper contains new and known results on homomorphisms that are close to regular. The main results are presented with proofs. © 2012 Springer Science+Business Media, Inc

Rings over which all modules are I0-modules. II

All right R-modules are I0-modules if and only if either R is a right SV-ring or R/I(2) (R) is an Artinian serial ring such that the square of the Jacobson radical of R/I(2) (R) is equal to zero. © 2009 Springer Science+Business Media, Inc