scholarly journals Good congruences on weakly ample semigroups

2021 ◽  
pp. 43-43
Author(s):  
Chunmei Gong ◽  
Lele Cui ◽  
Hui Wang
Keyword(s):  
Ample Semigroup ◽  
Normal Congruence

The concept of normal congruence on a weakly ample semigroup S is introduced and the maximum and minimum admissible congruences whose trace is the normal congruence on a weakly ample semigroup S are characterized in this paper. Some results about congruences on ample semigroups are generalized to weakly ample semigroups.

scholarly journals Surgical Treatment for Malunion of the Lateral Humeral Epicondyle with Posterior Subluxation of the Radial Head: A Case Report and Literature Review

2018 ◽  
Vol 2018 ◽  
pp. 1-4
Author(s):  
Koichi Yano ◽  
Yasunori Kaneshiro ◽  
Hideki Sakanaka
Keyword(s):  
Lateral Collateral Ligament ◽  
High Energy ◽  
Limited Range ◽  
Forearm Rotation ◽  
Collateral Ligament ◽  
Lateral Epicondyle ◽  
Limited Range Of Motion ◽  
Contracture Release ◽  
Normal Congruence ◽  
The Right

A 24-year-old right-handed man suffered right olecranon and lateral epicondylar fracture from high energy trauma. Fixation of olecranon was performed by a previous doctor. Three months after operation, he presented with limited range of motion (ROM) of the right elbow caused by malunion of the lateral epicondylar fracture and subluxation of the radiohumeral joint. Preoperative ROM of the right elbow was flexion 110° and extension −75°. Forearm rotation was pronation 85° and supination 65°. Fragment excision of the lateral epicondyle, which was 27 mm in length, and lateral collateral ligament repair using anchors were performed. Fourteen months postoperatively, contracture release of the elbow was performed. Twenty-four months postoperatively, radiograph of the elbow showed normal congruence without osteoarthritic changes and the ROM of the right elbow was flexion 120° and extension −35°. Forearm rotation was pronation 90° and supination 70°. In the surgical setting, in case of the size of the lateral epicondylar fragment is relatively large, the fragment should be fixed or lateral collateral ligament should be repaired when the instability of the elbow is found.

Locally ample semigroup algebras

2014 ◽  
Vol 07 (04) ◽  
pp. 1450067 ◽  
Author(s):  
Xiaojiang Guo ◽  
K. P. Shum
Keyword(s):  
Semigroup Algebra ◽  
Semigroup Algebras ◽  
Abundant Semigroup ◽  
Ample Semigroup

An idempotent-connected abundant semigroup S is a locally ample semigroup if for any idempotent e of S, the local submonoid eSe of S is an ample subsemigroup of S. Clearly, an ample semigroup is a locally ample semigroup. In this paper, it is proved that the semigroup algebra of a finite locally ample semigroup is isomorphic to the semigroup algebra of an associate primitive abundant semigroup. As an application of this result, we characterize Jacobson radicals of finite locally ample semigroup algebras.

scholarly journals A Study of Completely Inverse Paramedial AG-Groupoids

2021 ◽  
pp. 101-115
Author(s):  
Muhammad Rashad ◽  
Imtiaz Ahmad ◽  
Faruk Karaaslan
Keyword(s):  
Partial Order ◽  
Partial Orders ◽  
Left Identity ◽  
Normal Congruence ◽  
Paramedial Law ◽  
Congruence Pair

A magma S that meets the identity, xy·z = zy·x, ∀x, y, z ∈ S is called an AG-groupoid. An AG-groupoid S gratifying the paramedial law: uv · wx = xv · wu, ∀ u, v, w, x ∈ S is called a paramedial AGgroupoid. Every AG-grouoid with a left identity is paramedial. We extend the concept of inverse AG-groupoid [4, 7] to paramedial AG-groupoid and investigate various of its properties. We prove that inverses of elements in an inverse paramedial AG-groupoid are unique. Further, we initiate and investigate the notions of congruences, partial order and compatible partial orders for inverse paramedial AG-groupoid and strengthen this idea further to a completely inverse paramedial AG-groupoid. Furthermore, we introduce and characterize some congruences on completely inverse paramedial AG-groupoids and introduce and characterize the concept of separative and completely separative ordered, normal sub-groupoid, pseudo normal congruence pair, and normal congruence pair for the class of completely inverse paramedial AG-groupoids. We also provide a variety of examples and counterexamples for justification of the produced results.

scholarly journals FREE ADEQUATE SEMIGROUPS

2011 ◽  
Vol 91 (3) ◽  
pp. 365-390 ◽  
Author(s):  
MARK KAMBITES
Keyword(s):  
Inverse Semigroup ◽  
Word Problem ◽  
Explicit Description ◽  
Finitely Generated ◽  
Free Objects ◽  
Ample Semigroup ◽  
Free Inverse Semigroup ◽  
Adequate Semigroup

AbstractWe give an explicit description of the free objects in the quasivariety of adequate semigroups, as sets of labelled directed trees under a natural combinatorial multiplication. The morphisms of the free adequate semigroup onto the free ample semigroup and into the free inverse semigroup are realised by a combinatorial ‘folding’ operation which transforms our trees into Munn trees. We use these results to show that free adequate semigroups and monoids are 𝒥-trivial and never finitely generated as semigroups, and that those which are finitely generated as (2,1,1)-algebras have decidable word problem.

Tracing a Normal Congruence through an Optical System

1954 ◽  
Vol 44 (2) ◽  
pp. 146 ◽  
Author(s):  
M. Herzberger ◽  
E. Marchand
Keyword(s):  
Optical System ◽  
Normal Congruence

scholarly journals Some geometric properties of magneto-fluid flows

1982 ◽  
Vol 5 (2) ◽  
pp. 385-392
Author(s):  
S. S. Gangwar ◽  
Ram Babu
Keyword(s):  
Fluid Flows ◽  
Governing Equations ◽  
Geometric Properties ◽  
Normal Congruence ◽  
Stream Lines

By employing an anholonomic description of the governing equations, certain geometric results are obtained for a class of non-dissipative magnetofluid flows. The stream lines are geodesics on a normal congruence of the surfaces which are the Maxwellian surfaces.

scholarly journals PARTIAL ACTIONS OF INVERSE AND WEAKLY LEFT E-AMPLE SEMIGROUPS

2009 ◽  
Vol 86 (3) ◽  
pp. 355-377 ◽  
Author(s):  
VICTORIA GOULD ◽  
CHRISTOPHER HOLLINGS
Keyword(s):  
Unary Operation ◽  
Inverse Semigroups ◽  
Partial Transformation ◽  
Transformation Semigroups ◽  
Partial Action ◽  
Ample Semigroup

AbstractWe introduce partial actions of weakly left E-ample semigroups, thus extending both the notion of partial actions of inverse semigroups and that of partial actions of monoids. Weakly left E-ample semigroups arise very naturally as subsemigroups of partial transformation semigroups which are closed under the unary operation α↦α+, where α+ is the identity map on the domain of α. We investigate the construction of ‘actions’ from such partial actions, making a connection with the FA-morphisms of Gomes. We observe that if the methods introduced in the monoid case by Megrelishvili and Schröder, and by the second author, are to be extended appropriately to the case of weakly left E-ample semigroups, then we must construct not global actions, but so-called incomplete actions. In particular, we show that a partial action of a weakly left E-ample semigroup is the restriction of an incomplete action. We specialize our approach to obtain corresponding results for inverse semigroups.

Matrix representations of right ample semigroups

2015 ◽  
Vol 08 (03) ◽  
pp. 1550042 ◽  
Author(s):  
Junying Guo ◽  
Xiaojiang Guo ◽  
K. P. Shum
Keyword(s):  
Matrix Representation ◽  
Matrix Representations ◽  
Ample Semigroup ◽  
The Matrix

The properties of right ample semigroups have been extensively considered and studied by many authors. In this paper, we concentrate on the matrix representations of right ample semigroups. The (left; right) uniform matrix representation is initially defined. After some properties of left uniform matrix representations of a right ample semigroup are given, we prove that any irreducible left uniform representations of a right ample semigroup can be obtained by using an irreducible left uniform representation of some primitive right ample semigroup. In particular, a construction theorem of prime left uniform representation of right ample semigroups is established.

scholarly journals PROPER COVERS OF RESTRICTION SEMIGROUPS AND W-PRODUCTS

2012 ◽  
Vol 22 (03) ◽  
pp. 1250024 ◽  
Author(s):  
MÁRIA B. SZENDREI
Keyword(s):  
Ample Semigroup ◽  
Restriction Semigroup

Each factor semigroup of a free restriction (ample) semigroup over a congruence contained in the least cancellative congruence is proved to be embeddable into a W-product of a semilattice by a monoid. Consequently, it is established that each restriction semigroup has a proper (ample) cover embeddable into such a W-product.

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