广义morphic环

Generalized morphic rings

证明了当R是广义morphic环时,R是左Kasch环当且仅当R的任意极大左理想是一个零化子,也当且仅当R的任意极大左理想是由一个morphic元生成的主左理想.设R是环,R∝R是环R的特殊平凡扩张,a是R中的正则元,则a是R的广义左morphic元,当且仅当(a,0)是R∝R的广义左morphic元,也当且仅当(a,a)是R∝R的广义左morphic元.

If R is a generalized morphic ring, R is left Kasch ring if and only if every maximal left idea of R is an annihilator, and if and only if every maximal left idea of R is principal left idea generated by a morphic element. Let R be a ring, RocR be a special trivial extension, a be a regular element in R, then a is a generalized left morphic element in R, if and only if （a,0） is a generalized left morphic element in R∝R, and if and only if （a,a） is a generalized left morphic element in R∝R.