Multiplicative structures over sup-lattices
Multiplicatively idempotent semirings
Semirings are modifications of unitary rings where the additive reduct does not form a group in general, but only a monoid. We characterize multiplicatively idempotent semirings and Boolean rings as semirings satisfying particular identities. Further, we work with varieties of enriched semirings. We show that the variety of enriched multiplicatively idempotent semirings differs from the join of the variety of enriched unitary Boolean rings and the variety of enriched bounded distributive lattices....
Multipliers on a nearlattice
MV-algebras are categorically equivalent to a class of -semigroups
In the paper it is proved that the category of -algebras is equivalent to the category of bounded -semigroups satisfying the identity . Consequently, by a result of D. Mundici, both categories are equivalent to the category of bounded commutative -algebras.
MV-algebras with additive closure operators
Mодулярные структуры, в которых каждый элемент есть объединение циклов