scholarly journals KONDISI MINIMAL IDEAL KIRI TERURUT PADA SEMIGRUP TERNER TERURUT PARSIAL

2019 ◽  
Vol 15 (2) ◽  
pp. 280-287
Author(s):  
Andri Andri ◽  
Nasria Nacong
Keyword(s):  
Minimal Ideal ◽  
Ordered Semigroup ◽  
Partially Ordered ◽  
Multiplication Operation ◽  
Ternary Semigroup

Ternary semigroups 𝑇 is obtained from a nonempty set 𝑇 that given a mapping with a multiplication operation ternary that satisfied closed and associative properties. So, generally a ternary semigroup is an abstraction of a semigroup structure. Meanwhile, partially ordered ternary semigroups 𝑇 is an ordered semigroup 𝑇 that satisfies the properties for each 𝑎, 𝑏, 𝑐, 𝑑 ∈ 𝑇 if 𝑎 ≤ 𝑏 then (𝑎𝑐𝑑) ≤ (𝑏𝑐𝑑) and (𝑑𝑐𝑎) ≤ (𝑑𝑐𝑏). In a ternary semigroups there is also concept of left ideals. This study was conducted to examine the characteristics of ordered left ideals on partially ordered ternary semigroups. Furthermore, it will be discussed about the characteristics of minimal ordered left ideals on partially ordered semigroups.Keywords : Ternary Semigroups, Ordered Ternary Semigroups, Left Ideals, Ordered Left Ideals, Minimal of Ordered Left Ideals.

scholarly journals Continued fractions built from convex sets and convex functions

2015 ◽  
Vol 17 (05) ◽  
pp. 1550003 ◽  
Author(s):  
Ilya Molchanov
Keyword(s):  
Convex Functions ◽  
Continued Fractions ◽  
Convex Sets ◽  
Sufficient Conditions ◽  
Ordered Semigroup ◽  
Minkowski Addition ◽  
Partially Ordered ◽  
The Family ◽  
Sufficient Conditions For Convergence

In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalization of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

scholarly journals Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups

1981 ◽  
Vol 31 (3) ◽  
pp. 325-336 ◽  
Author(s):  
D. B. Mcalister
Keyword(s):  
Partial Order ◽  
Local Structure ◽  
Structure Theorem ◽  
Main Tool ◽  
Natural Partial Order ◽  
Ordered Semigroup ◽  
Ordered Group ◽  
Partially Ordered ◽  
Rees Matrix Semigroups ◽  
Matrix Semigroups

AbstractA partially ordered semigroup S is said to be a Dubreil-Jacotin semigroup if there is an isotone homomorphism θ of S onto a partially ordered group such that {} has a greatest member. In this paper we investigate the structure of regular Dubreil-Jacotin semigroups in which the imposed partial order extends the natural partial order on the idempotents. The main tool used is a local structure theorem which is introduced in Section 2. This local structure theorem applies to many other contexts as well.

The Arithmetic of the Quasi-Uniserial Semigroups without Zero

1971 ◽  
Vol 23 (3) ◽  
pp. 507-516 ◽  
Author(s):  
Ernst August Behrens
Keyword(s):  
Simple Semigroup ◽  
Disjoint Union ◽  
Maximal Subgroups ◽  
Ordered Semigroup ◽  
Partially Ordered ◽  
Completely Simple Semigroup ◽  
Image Position ◽  
Previous Paragraph ◽  
Completely Simple ◽  
Identity Elements

An element a in a partially ordered semigroup T is called integral ifis valid. The integral elements form a subsemigroup S of T if they exist. Two different integral idempotents e and f in T generate different one-sided ideals, because eT = fT, say, implies e = fe ⊆ f and f = ef ⊆ e.Let M be a completely simple semigroup. M is the disjoint union of its maximal subgroups [4]. Their identity elements generate the minimal one-sided ideals in M. The previous paragraph suggests the introduction of the following hypothesis on M.Hypothesis 1. Every minimal one-sided ideal in M is generated by an integral idempotent.

scholarly journals The Quantifier Semigroup for Bipartite Graphs

10.37236/610 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Leonard J. Schulman
Keyword(s):  
Bipartite Graph ◽  
Bipartite Graphs ◽  
The Other ◽  
Monotone Mappings ◽  
Ordered Semigroup ◽  
Partially Ordered

In a bipartite graph there are two widely encountered monotone mappings from subsets of one side of the graph to subsets of the other side: one corresponds to the quantifier "there exists a neighbor in the subset" and the other to the quantifier "all neighbors are in the subset." These mappings generate a partially ordered semigroup which we characterize in terms of "run-unimodal" words.

On a syntactically defined invariant of symbolic dynamics

2000 ◽  
Vol 20 (2) ◽  
pp. 501-516 ◽  
Author(s):  
WOLFGANG KRIEGER
Keyword(s):  
Symbolic Dynamics ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Topological Conjugacy ◽  
Ordered Semigroup ◽  
Partially Ordered

A partially ordered set that is invariantly associated to a subshift is constructed. A property of subshifts, also an invariant of topological conjugacy, is described. If this property is present in a subshift then the constructed partially ordered set is a partially ordered semigroup (with zero). In the description of these invariants the notion of context is instrumental.

scholarly journals ABSORBENT PENYARINGAN TERURUT DARI SEMIGRUP IMPLIKATIF

2015 ◽  
Vol 4 (1) ◽  
pp. 85
Author(s):  
Tutut Irla Multi
Keyword(s):  
Algebraic Structure ◽  
Binary Operation ◽  
Ordered Semigroup ◽  
Partially Ordered

The simplest algebraic structure is called groupoid, where groupoid isnonempty set with a binary operation. The groupoid which is associative is called asemigroup. A negatively partially ordered semigroup is a set A with a partial orderingand a binary operation. Such A is called implicative if there is an additional binary operation.In this paper will be reviewed the notion of absorbent ordered lters in implicativesemigroups. Then it will be studied the relations among ordered lters, absorbent orderedlters, and positive implicative ordered lters.

scholarly journals Maximum idempotents in naturally ordered regular semigroups

1983 ◽  
Vol 26 (2) ◽  
pp. 213-220 ◽  
Author(s):  
D. B. McAlister ◽  
R. McFadden
Keyword(s):  
Regular Semigroup ◽  
Partial Order ◽  
Natural Partial Order ◽  
Ordered Semigroup ◽  
Regular Semigroups ◽  
Partially Ordered ◽  
Image Position ◽  
Reverse Implication

We shall denote by ω the natural partial order on the idempotents E = E(S) of a regular semigroup S, so that in E,A partially ordered semigroup S(≦) is called naturally partially ordered [9] if the imposed partial order ≦ extends ω in the sense thatNo assumption is made about the reverse implication.

To the spectral theory of partially ordered sets

2018 ◽  
Vol 60 (3) ◽  
pp. 578-598
Author(s):  
Yu. L. Ershov ◽  
M. V. Schwidefsky
Keyword(s):  
Spectral Theory ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered
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