| A semiring is an algebra (S,+.) with two binary operations +and. such that both the additive reduct (S,+) and multipli -cative reduct (S, .) are semigroups connected by like-ring di -stributive laws, Corresponding to Left Clifford Semiring studied by Pastijn, Guo and Sen in paper[1],we introduce and study the so-called divided-semirings (left divided-semirings, rec -tangular divided-semirings), further discuss the distributive lattices of divided-semirings (left divided-semirings, rectangu -lar divided-semirings) and the member of MRGo Se which is the Mal'cev product of the semirings whose multiplicative re-ducts are rectangular groups and the member of St, investigate the relation between these semirings and their multiplicative reducts, obtain the characterizations of these semirings, give out their subdirect product decompositions. |
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