Let R be an associative ring not necessarily possessing an identity and （S,≤） a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having pr...Let R be an associative ring not necessarily possessing an identity and （S,≤） a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having property （F）.It is shown that M is a co-Hopfian left R-module if and only if [M<sup>S,≤</sup>]is a co-Hopfan left [[R<sup>S,≤</sup>]]-module.展开更多
This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows th...This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows that if η : P ?→ M is an ?- cover of M, then [ηS, ] : [PS, ] ?→ [MS, ] is an [?S, ]-cover of left [[RS, ]]-module ≤ ≤ ≤ ≤ ≤ [MS, ], where ? is a class of left R-modules and [MS, ] is the left [[RS, ]]-module of ≤ ≤ ≤ generalized inverse polynomials over a left R-module M. Also some properties of the injective cover of left [[RS, ]]-module [MS, ] are discussed. ≤展开更多
基金Research supported by National Natural Science Foundation of China,19671063
文摘Let R be an associative ring not necessarily possessing an identity and （S,≤） a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having property （F）.It is shown that M is a co-Hopfian left R-module if and only if [M<sup>S,≤</sup>]is a co-Hopfan left [[R<sup>S,≤</sup>]]-module.
基金the National Natural Science Foundation of China (No.10171082) the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China and NWNU-KJCXGC212.
文摘This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows that if η : P ?→ M is an ?- cover of M, then [ηS, ] : [PS, ] ?→ [MS, ] is an [?S, ]-cover of left [[RS, ]]-module ≤ ≤ ≤ ≤ ≤ [MS, ], where ? is a class of left R-modules and [MS, ] is the left [[RS, ]]-module of ≤ ≤ ≤ generalized inverse polynomials over a left R-module M. Also some properties of the injective cover of left [[RS, ]]-module [MS, ] are discussed. ≤
