Classical ideal semigroups (Q1977508)
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scientific article; zbMATH DE number 1448540
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classical ideal semigroups |
scientific article; zbMATH DE number 1448540 |
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Classical ideal semigroups (English)
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28 November 2000
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Complete lattices are considered. A complete lattice is called algebraic, if each of its elements is the join of some set of compact elements. An algebraic multiplication lattice is an algebraic lattice to which a further binary operation, called multiplication, is added. This multiplication is distributive with respect to the lattice operations. If an algebraic multiplication lattice is generated by a fixed submonoid of compact divisors, it is called an ideal monoid. If it is modular and satisfies a certain condition for prime ideals, it is a classical ideal semigroup. Properties of these concepts are studied.
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algebraic multiplication lattice
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algebraic lattice
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ideal monoid
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classical ideal semigroup
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