Then the relations among the classes of regular semigroups satisfying (IT), (IST), (QIT) and (QIST) are studied, and description for the classes of the ist_ (qist) _regular semigroups are given.
Then the relations among the classes of regular semigroups satisfying (IT),(IST),(QIT) and (QIST) are studied, and description for the classes of the ist_ (qist) _regular semigroups are given.