scholarly journals (λ,μ)-Fuzzy Version of Ideals, Interior Ideals, Quasi-Ideals, and Bi-Ideals

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Yuming Feng ◽  
P. Corsini
Keyword(s):  
Ordered Semigroup

We introduced(λ,μ)-fuzzy ideals,(λ,μ)-fuzzy interior ideals,(λ,μ)-fuzzy quasi-ideals, and(λ,μ)-fuzzy bi-ideals of an ordered semigroup and studied them. Whenλ=0andμ=1, we meet the ordinary fuzzy ones. This paper can be seen as a generalization of Kehayopulu and Tsingelis (2006), Kehayopulu and Tsingelis (2007), and Yao (2009).

On strongly convex L-fuzzy subsets of an ordered semigroup

2017 ◽  
Vol 32 (3) ◽  
pp. 1735-1744 ◽  
Author(s):  
Xiaokun Huang ◽  
Qingguo Li
Keyword(s):  
Ordered Semigroup ◽  
Strongly Convex ◽  
Fuzzy Subsets

scholarly journals Varieties of distributive lattices with unary operations I

1997 ◽  
Vol 63 (2) ◽  
pp. 165-207 ◽  
Author(s):  
H. A. Priestley
Keyword(s):  
Duality Theory ◽  
Algebraic Logic ◽  
Distributive Lattices ◽  
Ordered Semigroup ◽  
Finitely Generated ◽  
Left Multiplication ◽  
Unified Study

AbstractA unified study is undertaken of finitely generated varieties HSP () of distributive lattices with unary operations, extending work of Cornish. The generating algebra () is assusmed to be of the form (P; ∧, ∨, 0, 1, {fμ}), where each fμ is an endomorphism or dual endomorphism of (P; ∧, ∨, 0, 1), and the Priestly dual of this lattice is an ordered semigroup N whose elements act by left multiplication to give the maps dual to the operations fμ. Duality theory is fully developed within this framework, into which fit many varieties arising in algebraic logic. Conditions on N are given for the natural and Priestley dualities for HSP () to be essentially the same, so that, inter alia, coproducts in HSP () are enriched D-coproducts.

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.

Multipliers of certain convolution algebras over locally compact semigroups

1980 ◽  
Vol 87 (1) ◽  
pp. 51-59 ◽  
Author(s):  
D. G. Todd
Keyword(s):  
Ordered Semigroup ◽  
Real Numbers ◽  
Locally Compact ◽  
Multiplier Algebra ◽  
Similar Work ◽  
Convolution Algebras ◽  
Compact Semigroups ◽  
Integrable Functions ◽  
Locally Compact Semigroups

In this paper we extend a result of Johnson and Lahr(3), which characterizes the multiplier algebra of L1(a, b) (the algebra of Lebesgue integrable functions on the interval of real numbers from a to b, under order convolution) to the L1 algebra of a general totally ordered semigroup. Similar work has been done in (l), but under more restrictive conditions.

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 Fuzzy ideals of ordered semigroups with fuzzy orderings

2016 ◽  
Vol 14 (1) ◽  
pp. 841-856
Author(s):  
Xiaokun Huang ◽  
Qingguo Li
Keyword(s):  
Fuzzy Relation ◽  
Lattice Structures ◽  
Ordered Semigroup ◽  
Fuzzy Subset ◽  
Ordered Semigroups ◽  
Fuzzy Orderings

AbstractThe purpose of this paper is to introduce the notions of ∈, ∈ ∨qk-fuzzy ideals of a fuzzy ordered semigroup with the ordering being a fuzzy relation. Several characterizations of ∈, ∈ ∨qk-fuzzy left (resp. right) ideals and ∈, ∈ ∨qk-fuzzy interior ideals are derived. The lattice structures of all ∈, ∈ ∨qk-fuzzy (interior) ideals on such fuzzy ordered semigroup are studied and some methods are given to construct an ∈, ∈ ∨qk-fuzzy (interior) ideals from an arbitrary fuzzy subset. Finally, the characterizations of generalized semisimple fuzzy ordered semigroups in terms of ∈, ∈ ∨qk-fuzzy ideals (resp. ∈, ∈ ∨qk-fuzzy interior ideals) are developed.

Residuated Completely Simple Semigroups

2014 ◽  
Vol 21 (02) ◽  
pp. 181-194
Author(s):  
T. S. Blyth ◽  
G. A. Pinto
Keyword(s):  
Cyclic Group ◽  
Simple Semigroup ◽  
Lexicographic Order ◽  
Ordered Semigroup ◽  
Completely Simple Semigroup ◽  
Completely Simple Semigroups ◽  
Completely Simple

We consider particular compatible orders on a given completely simple semigroup Sx=M(〈x〉; I ,Λ;P) where 〈x〉 is an ordered cyclic group with x > 1 and P11=x-1. Of these, only the lexicographic and bootlace orders yield residuated semigroups. With the lexicographic order, Sx is orthodox and has a biggest idempotent. With the bootlace order, the maximal idempotents of Sx are identified by specific locations in the sandwich matrix. In the orthodox case there is also a biggest idempotent and, for sandwich matrices of a given size, uniqueness up to ordered semigroup isomorphism is established.

Sign in / Sign up

Export Citation Format

Share Document