Related Experiment Video
Updated: Jan 22, 2026

Depletion of Specific Cell Populations by Complement Depletion
Published on: February 5, 2010
Ideals and their complements in commutative semirings
Ivan Chajda1, Helmut Länger1,2
11Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic.
Abstract:
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 I of is a complement of I. 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.
Related Concept Videos
Ideal Solutions
The Ideal Transformer
Ampere's Law forms the basis of understanding the magnetic field within the transformer. It states that the integral of the magnetic field intensity's tangential...
Complement System
Complementation Tests
Organisms heterozygous for different mutations are crossed pairwise in all combinations. If present on different genes, the mutations can complement each other by providing the missing...
The Ideal Diode
Ideal Gas Equation

