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 Clifford semigroups and monotonicity

1985 ◽  
Vol 32 (1) ◽  
pp. 83-92
Author(s):  
T.E. Hays
Keyword(s):  
Algebraic Structure ◽  
Binary Operation ◽  
Monotone Function ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Clifford Semigroups ◽  
Necessary And Sufficient

A semigroup S is said to be monotone if its binary operation is a monotone function from S × S into S. This paper utilizes some of the known algebraic structure of Clifford semigroups, semigroups which are unions of groups, to study topological Clifford semigroups which are monotone. It is shown that such semigroups are preserved under products, homomorphisms, and, under certain conditions, closures. Necessary and sufficient conditions for monotonicity of groups, paragroups, bands, compact orthodox Clifford semigroups, and compact bands of groups are developed.

Summary of Elements of Algebraic Theory

1995 ◽  
Author(s):  
F. Iachello ◽  
R. D. Levine
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Algebraic Structure ◽  
Binary Operation ◽  
Algebraic Theory ◽  
Quantum Mechanical ◽  
Ordinary Quantum

Algebraic theory makes use of an algebraic structure. The structure appropriate to ordinary quantum mechanical problems is that of a Lie algebra. We begin this chapter with a brief review of the essential concepts of Lie algebras. The binary operation (“multiplication”) in the Lie algebra is that of taking the commutator. As usual, we denote the commutator by square brackets, [A, B] = AB - BA. A set of operators {X} is a Lie algebra when it is closed under commutation.

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.

Injective Hulls of Semilattices

1970 ◽  
Vol 13 (1) ◽  
pp. 115-118 ◽  
Author(s):  
G. Bruns ◽  
H. Lakser
Keyword(s):  
Upper Bound ◽  
Partially Ordered Set ◽  
Binary Operation ◽  
Ordered Set ◽  
Upper Bounds ◽  
Partial Ordering ◽  
Partially Ordered ◽  
Image Position ◽  
Injective Hulls

A (meet-) semilattice is an algebra with one binary operation ∧, which is associative, commutative and idempotent. Throughout this paper we are working in the category of semilattices. All categorical or general algebraic notions are to be understood in this category. In every semilattice S the relationdefines a partial ordering of S. The symbol "∨" denotes least upper bounds under this partial ordering. If it is not clear from the context in which partially ordered set a least upper bound is taken, we add this set as an index to the symbol; for example, ∨AX denotes the least upper bound of X in the partially ordered set A.

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.

Convex structures in a new kind of ordered fuzzy group1

2020 ◽  
Vol 39 (3) ◽  
pp. 4245-4257
Author(s):  
Hongping Liu ◽  
Ruiju Wei ◽  
Qian Ge
Keyword(s):  
Convex Hull ◽  
Binary Operation ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Convex Subgroup ◽  
Partially Ordered ◽  
Convex Structure ◽  
Fuzzy Group ◽  
Fuzzy Setting ◽  
Convex Spaces

By means of a fuzzy binary operation defined on partially ordered sets, a new kind of ordered fuzzy group is proposed in this paper. Some properties of this ordered fuzzy group are studied. Following that, its substructures, such as subgroup and convex subgroup, as well as its homomorphisms, along with their properties are explored. It is shown that each family of these substructures forms a convex structure, where the convex hull of a subset is exactly the (convex) subgroup generated by itself, and the homomorphisms between two ordered fuzzy groups are convexity-preserving mappings between the corresponding convex spaces. In addition, when these substructures are extended to fuzzy setting, several L-convex structures are constructed and investigated.

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.

Orders on magmas and computability theory

2018 ◽  
Vol 27 (07) ◽  
pp. 1841001
Author(s):  
Trang Ha ◽  
Valentina Harizanov
Keyword(s):  
Algebraic Structure ◽  
Knot Theory ◽  
Binary Operation ◽  
Computability Theory ◽  
Linear Ordering ◽  
Natural Numbers ◽  
Right Order

We investigate algebraic and computability-theoretic properties of orderable magmas. A magma is an algebraic structure with a single binary operation. A right order on a magma is a linear ordering of its domain, which is right-invariant with respect to the magma operation. We use tools of computability theory to investigate Turing complexity of orders on computable orderable magmas. A magma is computable if it is finite, or if its domain can be identified with the set of natural numbers and the magma operation is computable. Interesting orderable magmas that are not even associative come from knot theory.

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.

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