On the lattice of quasi-filters of left congruence on a principal left ideal semigroups
M. Ya. Komarnitskiy, Roman Oliynyk · Matematychni Studii · 2011
On the lattice of quasi-filters of left congruence on a principal left ideal semigroups, Mat.Stud.35 (2011), 128-130.The lattice structure on quasi-filters of left congruence on a principal left ideal semigroup are described.Н. Я. Комарницкий, Р. Н. Олийнык.О структуре решетки квазифильтров левых конгруэнции над полугруппой главных левых идеалов // Мат.Студiї.-2011.-Т.35, №2.-C.128-130.Описывается строение решетки квазифильтров левых конгруэнций над полугруппой главных левых идеалов.Torsion theory, as mentioned by B. Stenstrom, is an important tool in the study of the quotient structure of rings.The concept of torsion theory for S-acts was introduced by J. K. Luedeman [4] in 1983.Recently, R. Zhang, W. Gao, F. Xu [8] introduced the concept of quasi-filter of right congruence on a semigroup S, and established a close relation between these quasi-filters and the hereditary torsion theory of S-acts.Their results have a new influence on the study of the torsion theories of S-acts [5], [7].For rings the lattice structure on filters are considered in the book J. S. Golan [1].We recall some necessary definitions.Throughout this paper, S is always a multiplicative semigroup with 0 and 1.The terminology and definitions that are not given in this paper can be found in [3].Denoted by Con(S) the set of all left congruence on S.