Γ - semigroup generated by a semigroup Sumanto, Y D; Aziz, A; Solikhin ...
Journal of physics. Conference series,
04/2020, Volume:
1524, Issue:
1
Journal Article
Peer reviewed
Open access
In Γ - semigroup S, the element of Γ maybe a binary operation in S. Every element of any semigroupS can define a binary operation in S. A collection of binary operations defined of the element of S ...generates Γ - semigroup S.
In this article, we shall give the concepts of bipolar fuzzy weakly interior ideals of semigroups, and we provide some interesting properties of bipolar fuzzy weakly interior ideals of semigroups. ...The relationship between bipolar fuzzy weakly interior ideals and bipolar fuzzy left (right) ideals, and the relationship between bipolar fuzzy weakly interior ideals and bipolar fuzzy interior ideals are also discussed. In the results, we proceed to characterize some semigroups by using bipolar fuzzy weakly interior ideals. Finally, we discuss the image and pre-image of bipolar fuzzy weakly interior ideals of semigroups.
On ð" -regular semigroups Feng, Xinyang
Open mathematics (Warsaw, Poland),
01/2018, Volume:
16, Issue:
1
Journal Article
Peer reviewed
Open access
In this paper, we give some characterizations of ð" -regular semigroups and show that the class of ð" -regular semigroups is closed under the direct product and homomorphic images. Furthermore, we ...characterize the ð" -subdirect products of this class of semigroups and study the E-unitary ð" -regular covers for ð" -regular semigroups, in particular for those whose maximum group homomorphic image is a given group. As an application of these results, we claim that the similar results on V-regular semigroups also hold.
Conjugacy in inverse semigroups Araújo, João; Kinyon, Michael; Konieczny, Janusz
Journal of algebra,
09/2019, Volume:
533
Journal Article
Peer reviewed
Open access
In a group G, elements a and b are conjugate if there exists g∈G such that g−1ag=b. This conjugacy relation, which plays an important role in group theory, can be extended in a natural way to inverse ...semigroups: for elements a and b in an inverse semigroup S, a is conjugate to b, which we will write as a∼ib, if there exists g∈S1 such that g−1ag=b and gbg−1=a. The purpose of this paper is to study the conjugacy ∼i in several classes of inverse semigroups: symmetric inverse semigroups, McAllister P-semigroups, factorizable inverse monoids, Clifford semigroups, the bicyclic monoid, stable inverse semigroups, and free inverse semigroups.
It has been known for a long time that every finite orthodox completely regular semigroup has a finite basis of identities, and that every finite central completely simple semigroup has a finite ...basis of identities. In the present paper, a common generalization of these two facts is established. It is shown that every finite central locally orthodox completely regular semigroup has a finite basis of identities. The proof of this latter fact which is presented in this paper employs significantly the celebrated theorem of Libor Polák on the structure of the lattice of all varieties of completely regular semigroups.
A recent paper studied an inverse submonoid
M
n
of the rook monoid, by representing the nonzero elements of
M
n
via certain triplets belonging to
Z
3
. In this note, we allow the triplets to belong ...to
R
3
. We thus study a new inverse monoid
M
¯
n
, which is a supermonoid of
M
n
. We point out similarities and find essential differences. We show that
M
¯
n
is a noncommutative, periodic, combinatorial, fundamental, completely semisimple, and strongly
E
∗
-unitary inverse monoid.
In 1961, L.M. Gluskin proved that a given set with an arbitrary nontrivial quasiorder is determined up to isomorphism or anti-isomorphism by the semigroup of all isotone transformations of , i.e., ...the transformations of preserving . Subsequently, L.M. Popova proved a similar statement for the semigroup of all partial isotone transformations of ; here the relation does not have to be a quasiorder but can be an arbitrary nontrivial reflexive or antireflexive binary relation on the set . In the present paper, under the same constraints on the relation , we prove that the semigroup of all isotone binary relations (set-valued mappings) of determines up to an isomorphism or anti-isomorphism as well. In addition, for each of the conditions , , and , we enumerate all -ary relations satisfying the given condition.
We introduce the notion of accurate foundation sets and the accurate refinement property for right LCM semigroups. For right LCM semigroups with this property, we derive a more explicit presentation ...of the boundary quotient. In the context of algebraic dynamical systems, we also analyse finiteness properties of foundation sets which lead us to a very concrete presentation. Based on Starling's recent work, we provide sharp conditions on certain algebraic dynamical systems for pure infiniteness and simplicity of their boundary quotient.
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