A solution is given for the word problem for free idempotent distributive semirings. Using this solution the lattice L(ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns...A solution is given for the word problem for free idempotent distributive semirings. Using this solution the lattice L(ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns out that L(ID) is isomorphic to the direct product of a four-element lattice and a lattice which is itself a subdirect product of four copies of the lattice L (B) of all band varieties. Therefore L(ID) is countably infinite and distributive. Every subvariety of ID is finitely based.展开更多
Semirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent semirings, and in particular, the variety of distributive lattices. Various stru...Semirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent semirings, and in particular, the variety of distributive lattices. Various structure theorems are established which bring insight into the structure of the lattice of subvarieties of S.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 197610O4)the Provincial Applied Fundamental Research Foundation of Yunnan (96a001z).
文摘A solution is given for the word problem for free idempotent distributive semirings. Using this solution the lattice L(ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns out that L(ID) is isomorphic to the direct product of a four-element lattice and a lattice which is itself a subdirect product of four copies of the lattice L (B) of all band varieties. Therefore L(ID) is countably infinite and distributive. Every subvariety of ID is finitely based.
基金Guo Yuqi was supported by the National Natural Science Foundation of China (Grant No. 10071068) the Provincial Applied Fundamental Research Foundation of Yunnan Province of China.
文摘Semirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent semirings, and in particular, the variety of distributive lattices. Various structure theorems are established which bring insight into the structure of the lattice of subvarieties of S.
