Ternary Semigroups Research Articles

Interval Valued Intuitionistic (S, T)- Fuzzy Ideals of Ternary Semigroups

In this paper, the concept of interval valued intuitionistic fuzzy ternary subsemigroup (ideal) of a ternary semigroup with respect to interval t-norm T and interval t-conorm S is given and the characteristic properties are described. We characterized some other classes of ternary semigroups by the properties these interval valued intuitionistic fuzzy ternary subsemigroup (ideal) of a ternary semigroup. The homomorphic image and inverse image are also investigated.

Interval Valued Intuitionistic (S – , T– )- Fuzzy Ideals of Ternary Semigroups

In this paper, the concept of interval valued intuitionistic fuzzy ternary subsemigroup (ideal) of a ternary semigroup with respect to interval t-norm T and interval t-conorm S is given and the characteristic properties are described. We characterized some other classes of ternary semigroups by the properties these interval valued intuitionistic fuzzy ternary subsemigroup (ideal) of a ternary semigroup. The homomorphic image and inverse image are also investigated.

T-ROUGH IDEALS IN TERNARY SEMIGROUPS

The purpose of this paper is to introduce and discuss the concept of T-rough ternary subsemigroups, T-rough ideals, T-rough bi-ideals and T-rough interior ideals in ternary semigroups. AMS Subject Classification: 20N10

Some properties of hyperideals in ternary semihypergroups

Abstract Ternary semihypergroups are algebraic structures with one ternary associative hyperoperation. In this paper we give some properties of left (right) and lateral hyperideals in ternary semihypergroups. We introduce the notion of left simple, lateral simple, left (0-)simple and lateral 0-simple ternary semihypergroups and characterize the minimality and maximality of left (right) and lateral hyperideals in ternary semihypergroups. The relationship between them is investigated in ternary semihypergroups extending and generalizing the analogues results for ternary semigroups.

Chained Commutative Ternary Semigroups

In this paper, the terms chained ternary semigroup, cancellable clement , cancellative ternary semigroup, A-regular element, π- regular element, π- invertible element, noetherian ternary semigroup are introduced. It is proved that in a commutative chained ternary semigroup T, i) if P is a prime ideal of T and

Prime Radicals in Ternary Semigroups

In this paper the terms completely prime ideal, prime ideal, m-system. globally idempotent , semi simple elements of a ternary semigroup are Introduced. It is proved that an ideal A of a ternary semigroup T is completely prime if and only if T\A is either sub semigroup of T or empty. It is proved that if T is a globally idempotent ternary semigroup then every maximal ideal of T is a prime ideal of T. In this paper the terms completely semiprime ideal, semiprime ideal, n-system, d-system and i-system are introduced. It is proved that the non-empty intersection of any family of a completely prime ideal and prime ideal of a ternary semigroup T is a completely semiprime ideal of T. It is also proved that an ideal A of a ternary semigroup T is completely semiprime if and only if T\A is a d-system of T or empty. It is proved that if N is an n-system in a ternary semigroup T and a

Green's Condition and Green-Kehayopulu Relations on $le$-Ternary Semigroups

We introduce the concept of the Green-Kehayopulu relations in $le$-ternary semigroups mimics the definition of the Green-Kehayopulu relations in $le$-semigroups that was introduced in 2002 by Petro and Pasku [3] and investigate the Green-Kehayopulu relations in $le$-ternary semigroups.

On Ordered Ternary Semigroups

Abstract. We introduce the concepts of ordered quasi-ideals, ordered bi-ideals in anordered ternary semigroup and study their properties. Also regular ordered ternarysemigroup is de ned and several ideal-theoretical characterizations of the regular orderedternary semigroups are furnished. 1. IntroductionThe literature of a ternary algebraic system was introduced by D. H. Lehmer[3] in 1932. He investigated certain ternary algebraic systems called triplexes whichturn out to be ternary groups. The notion of ternary semigroup was known toS.Banach. He showed by an example that ternary semigroup does not necessar-ily reduce to an ordinary semigroup. In [6] M. L. Santiago developed the theory ofternary semigroups. He focused his attention mainly to the study of regular ternarysemigroups, bi-ideals and ideals in ternary semigroups. The semigroup Z of all in-tegers under multiplication which plays a vital role in the literature of semigroup.The subset Z + of all positive integers of Z is a semigroup under multiplication.Now if we consider the subset Z of all negative integers of Z, then it is not a semi-group under multiplication. Taking these facts in mind D. H. Lehmer [3] introducedthe notion of ternary semigroup. Z is a natural example of a ternary semigroupunder the ternary multiplication. N. Kehayopulu in [5] developed the theory ofpo-semigroups. He mainly studied regular po-semigroups, ideals and bi-ideals inpo-semigroups. In 1999, Sang Keun Lee and Seong Gon Kang [4] gave charac-

Pure Fuzzy Ideals in Ternary semigroups

In this paper we initiate the study of pure fuzzy ideals in ternary semigroups. We introduce the notions of purely fuzzy maximal and purely fuzzy prime ideals of a ternary semigroup T. We also characterize those ternary semigroups for which each fuzzy ideal is weakly pure.

Intuitionistic Fuzzy Points and Ideals of Ternary Semigroups

In this paper, we consider the intuitionistic fuzzy sets in a ternary semigroup and the corresponding sets of intuitionistic fuzzy points. We analyze some relations between the intuitionistic fuzzy ideals of a ternary semigroup \(T\) and the sets of intuitionistic fuzzy points.

Fuzzy Ideals of Ternary Semigroups

In this paper, we introduce fuzzy ideals of ternary semigroups and study their related properties. Here we define fuzzy left (right, lateral) ideals of ternary semigroups and characterize regular and intra-regular ternary semigroups by using the concept of fuzzy ideals of ternary semigroups.

Minimal and maximal bi-ideals in ordered ternary semigroups

For estimating a time-varying signal frequency, an alternative estimator with a finite memory structure is proposed. The proposed estimator is developed under a maximum likelihood criterion using only the most recent finite observations on the window. The proposed estimator is first represented in a batch form, and then in a recursive form for computational advantage. The proposed estimator is shown to have good inherent properties, such as unbiasedness and deadbeat. Finally, via computer simulation and comparison, the proposed approach is shown to outperform remarkably the variable forgetting factor (VFF) Kalman filtering approach. Key words: Estimating signal frequency, finite memory structure, unbiasedness, deadbeat.

Ternary γ-homomorphisms and ternary γ-derivations on ternary semigroups

In this paper, we introduce the notions of γ-homomorphism and γ-derivation of a ternary semigroup and investigate γ-homomorphism and γ-derivations on ternary semigroup associated with the following functional in-equality |f([xyz]) - f(x) - f(y) - f(z)| ≤ φ(x, y, z) and |f([xxx]) - 3f(x)| ≤ φ(x, x, x), respectively.

A description of n-ary semigroups polynomial-derived from integral domains

We provide a complete classification of the n-ary semigroup structures defined by polynomial functions over infinite commutative integral domains with identity, thus generalizing Głazek and Gleichgewicht’s classification of the corresponding ternary semigroups.

Ternary Weighted Function and Beurling Ternary Banach Algebra l1ω(S)

Let S be a ternary semigroup. In this paper, we introduce our notation and prove some elementary properties of a ternary weight function ω on S. Also, we make ternary weighted algebra and show that is a ternary Banach algebra.

Some Ideals of Ternary Semigroups

Some Ideals of Ternary SemigroupsIn this paper we characterize different types of ideals of ternary semigroup and study some interesting properties of these ideals of ternary semigroup.

Ternary semigroups

Ternary semigroups

Fuzzy Ideals and Fuzzy Filters of Ordered Ternary Semigroups

The notion of ternary semigroups was introduced by Lehmer in 1932 and that of fuzzy sets by Zadeh in 1965. Anysemigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup.A partially ordered semigroup T is called an ordered ternary semigroup if for all x1; x2; x3; x4 2 T; x1  x2 impliesx1x3x4  x2x3x4; x3x1x4  x3x2x4 and x3x4x1  x3x4x2. In this paper, we study fuzzy ternary subsemigroups (left ideals,right ideals, lateral ideals, ideals) and fuzzy left filters (right filters, lateral filters, filters) of ordered ternary semigroups.

On ordered ideal extensions of ordered ternary semigroups

Our work in this paper is to introduce the concept of ordered ideal extensions in ordered ternary semigroups. The connection between an ordered ideal extensions and some congruences in ordered ternary semigroups is considered.

PRIME IDEALS IN TERNARY SEMIGROUPS

In this paper we define prime, semiprime and irreducible ideals in ternary semigroups. We also define semisimple ternary semigroups and prove that a ternary semigroup is semisimple if and only if each of its ideals is semiprime.