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"I liked the algebraic way of looking at things.
I’m additionally fascinated when the algebraic method is applied to infinite objects”.

Irwing Kaplansky

On the lattice of quasi-filters of left congruences on a Clifford semigroups

 

Roman Oliynyk

Associate Professor
Lviv National Agrarian University

 

 

 

Abstract:

The lattice structure on quasi-filters of left congruences on a Clifford semigroups are described.

Theorem. Let S is a Clifford semigroup. Then the lattice of quasi-filters of left congruences has no trivial quasi-filter if and only if S is a group G, such that the normal subgroups of G form a chain under the set inclusion.

 

 

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Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
1 Universytetska Str., 79000 Lviv, Ukraine
Tel: (+380 322) 394 172
E-mail: oromaniv at franko.lviv.ua

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