(m,n)-凝聚模与(m,n)-半遗传模

(m,n)-Coherent Modules and(m,n)-Semihereditary Modules

通过类比凝聚模、(m,n)-凝聚环和半遗传环的概念与性质,给出了(m,n)-凝聚模和(m,n)-半遗传模的概念,并研究了在一般环的条件下(m,n)-凝聚模和(m,n)-半遗传模的性质.还通过(m,n)-M-平坦模和(m,n)-M-内射模给出了(m,n)-凝聚模和(m,n)-半遗传模的一些等价刻画.

In this paper,the concepts of(m,n)-coherent modules and(m,n)-semihereditary modules are given by analogy to the concepts and properties of coherent modules,(m,n)-coherent rings and semihereditary rings,and the properties of(m,n)-coherent modules and(m,n)-semihereditary modules under the condition of general rings are studied.Some equivalent characterizations of(m,n)-coherent modules and(m,n)-semihereditary modules are also given by(m,n)-M-flat modules and(m,n)-M-injective modules.