We study conditions under which the lattice of ideals of a given a commutative semiring is complemented. At first we check when the annihilator of a given ideal of is a complement of . Further, we study complements of annihilator ideals. Next we investigate so-called Łukasiewicz semirings. These form a counterpart to MV-algebras which are used in quantum structures as they form an algebraic semantic of many-valued logics as well as of the logic of quantum mechanics. We describe ideals and congruence kernels of these semirings with involution. Finally, using finite unitary Boolean rings, a construction of commutative semirings with complemented lattice of ideals is presented.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6559127 | PMC |
| http://dx.doi.org/10.1007/s00500-018-3493-2 | DOI Listing |
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