Subtraction-like operations in nearsemilattices

• Autorzy: Cirulis J.
• Języki publikacji: EN

Abstrakty

EN

A nearsemilattice is a poset having the upper-bound property. A binary operation — on a poset with the least element 0 is said to be subtraction-like if x ≤ y if and only if x — y = 0 for all x, y. Associated with such an operation is a family of partial operations lp defined by lp(x) := p— x on every initial segment [0, p]; these operations are thought of as local (sectional) complementations of some kind. We study several types of subtraction-like operations, show that each of these operations can be restored in a uniform way from the corresponding local complementations, and state some connections between properties of a (sufficiently strong) subtraction on a nearsemilattice and distributivity of the latter.

Słowa kluczowe

EN

Brouwerian complementation; de Morgan complementation; distributive; Galois connection; nearsemilattice; pseudocomplementation; relative pseudocomplementation; sectional; subtraction; weak BCK-algebra

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 4
• Strony: 725--738
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Cirulis J.

• Department of Mathematics University of Latvia Zellu str., 8, Riga, LV-1002, Latvia,

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