Generalized Left Clifford Semirings.

In the paper, the concepts of left skew-ring and generalized left Clifford semiring are firstly introduced. Secondly, some of their equivalence characterizations are given. And then, a spined product decomposition of the generalized left Clifford semiring is obtained. Also, a necessary and sufficient condition for a generalized left Clifford semiring to be expressed into a strong b-lattice of left skew-rings is finally given. As a consequence, some results about Clifford semirings in [14] and left Clifford semirings in [8] are strengthened and extended. [ABSTRACT FROM AUTHOR]