Quasiresiduals in Semigroups with Natural Partial Order
Keyword(s):
A semigroup (S, ·) is called right (left) quasiresiduated if for any a, b in S there exists x in S such that ax ≤S b (xa ≤S b) with respect to the natural partial order ≤S of S. This concept has its origin in the theory of residuated semigroups, but can also be seen as a generalization of the right (left) simplicity of semigroups. It is first studied for totally-, resp., trivially-ordered semigroups, and then for semigroups with idempotents. In particular, the cases when (S, ≤S) is directed downwards and when S contains a zero (with respect to a more restrictive definition) are dealt with. Throughout, examples are given; in total, 30 classes of (often well-known) semigroups of this kind are specified.
Keyword(s):
2014 ◽
Vol 91
(2)
◽
pp. 264-267
◽
Keyword(s):
2021 ◽
Vol 1764
(1)
◽
pp. 012046
Keyword(s):
2014 ◽
Vol 91
(1)
◽
pp. 104-115
◽
Keyword(s):
1973 ◽
Vol 15
(4)
◽
pp. 441-460
◽
Keyword(s):
1972 ◽
Vol 13
(4)
◽
pp. 451-455
◽
Keyword(s):
1980 ◽
Vol 29
(4)
◽
pp. 475-503
◽
2019 ◽
Vol 19
(01)
◽
pp. 2050011
◽
Keyword(s):
2018 ◽
Vol 17
(1)
◽
pp. 37-43
Keyword(s):
1982 ◽
Vol 33
(1)
◽
pp. 92-101
◽
Keyword(s):