Ordered power ternary semigroups

2021 ◽  
Author(s):  
S. Kar ◽  
A. Roy ◽  
I. Dutta
Keyword(s):  
Ternary Semigroup

We consider a power ternary semigroup [Formula: see text] associated with a ternary semigroup [Formula: see text] and study some properties of [Formula: see text] by using the corresponding properties of [Formula: see text]. After that we study the notion of ordered power ternary semigroup and our main aim is to establish some interconnection between the properties of a ternary semigroup [Formula: see text] and the associated ordered ternary semigroup [Formula: see text].

Global determinism of ternary semilattices

2019 ◽  
Vol 13 (04) ◽  
pp. 2050083
Author(s):  
S. Kar ◽  
I. Dutta
Keyword(s):  
Ternary Semigroup ◽  
Global Determinism

The global determinism of a ternary semigroup [Formula: see text] is the set of all nonempty subsets of [Formula: see text], denoted by [Formula: see text] equipped with the naturally defined multiplication. A class [Formula: see text] of ternary semigroups is said to be globally determined if any two members [Formula: see text] and [Formula: see text] of [Formula: see text] with isomorphic globals are themselves isomorphic i.e. [Formula: see text] implies that [Formula: see text] for any two ternary semigroups [Formula: see text] and [Formula: see text] in the class [Formula: see text]. In this paper, we mainly discuss that the class of all ternary semilattices are globally determined.

PRIME IDEALS IN TERNARY SEMIGROUPS

2009 ◽  
Vol 02 (01) ◽  
pp. 141-154 ◽  
Author(s):  
Muhammad Shabir ◽  
Shahida Bashir
Keyword(s):  
Prime Ideals ◽  
Ternary Semigroup

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.

scholarly journals On Characterization of Open Sets in Euclidean Spaces

2018 ◽  
Vol 22 ◽  
pp. 01007
Author(s):  
Firudin Kh. Muradov
Keyword(s):  
Topological Spaces ◽  
Euclidean Spaces ◽  
Abstract Characterization ◽  
Ternary Semigroup ◽  
Associative Law ◽  
Open Maps

A ternary semigroup is a nonempty set T together with a ternary oper- ation [abc] satisfying the associative law [[abc] de] = [a [bcd] e] = [ab [cde]] for all a, b, c, d, e ε T. A map f between topological spaces X and Y is called open if the image of each set open in X is open in Y. The pur- pose of this paper is to give an abstract characterization of the ternary semigroups of open maps defined on open sets in Euclidean n-spaces.

scholarly journals Some Ideals of Ternary Semigroups

2011 ◽  
Vol 57 (2) ◽  
pp. 247-258
Author(s):  
S. Kar ◽  
B. Maity
Keyword(s):  
Different Types ◽  
Ternary Semigroup

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.

scholarly journals STRONGLY PRIME RADICALS OF A TERNARY SEMIGROUP

2017 ◽  
Vol 116 (1) ◽  
Author(s):  
M.P. Seetha ◽  
Y. Sarala ◽  
A. Anjaneyulu ◽  
P. Bindu
Keyword(s):  
Ternary Semigroup

scholarly journals Ternary semigroups of topological transformations

2021 ◽  
Vol 102 (2) ◽  
pp. 84-91
Author(s):  
F.Kh. Muradov ◽  
Keyword(s):  
Euclidean Spaces ◽  
Finite Dimensional ◽  
Ternary Operation ◽  
Ternary Semigroup ◽  
Topological Transformations

A ternary semigroup is a nonempty set with a ternary operation which is associative. The purpose of the present paper is to give a characterization of open sets of finite-dimensional Euclidean spaces by ternary semigroups of pairs of homeomorphic transformations and extend to ternary semigroups certain results of L.M. Gluskin concerned with semigroups of homeomorphic transformations of finite-dimensional Euclidean spaces.

Globally determined ternary semigroups

2017 ◽  
Vol 10 (03) ◽  
pp. 1750038
Author(s):  
S. Kar ◽  
I. Dutta
Keyword(s):  
Principal Ideal ◽  
Ternary Semigroup ◽  
Special Classes

Let [Formula: see text] be the set of all nonempty subsets of a ternary semigroup [Formula: see text]. Then [Formula: see text] is a ternary semigroup with respect to the ternary multiplication defined by [Formula: see text] for all [Formula: see text]. If [Formula: see text] and [Formula: see text] are isomorphic ternary semigroups, then the corresponding power ternary semigroups [Formula: see text] and [Formula: see text] are obviously isomorphic. It is quite natural to ask whether the converse is true, i.e. is it true that for any ternary semigroups [Formula: see text] and [Formula: see text], [Formula: see text] implies that [Formula: see text]? If the class [Formula: see text] of algebra has this property, we say that [Formula: see text] is a globally determined class. In this paper, we provide some class of globally determined ternary semigroups. We show that all ternary semigroups are not globally determined but some special classes of ternary semigroups are globally determined. We show that the class of finite left (right) zero ternary semigroups, ternary groups and principal ideal (P. I.) ternary semigroups are globally determined but the class of involution ternary semigroups is not globally determined.

Note on topological ternary semigroup

2020 ◽  
pp. 2150086
Author(s):  
S. Samanta ◽  
S. Jana ◽  
S. Kar
Keyword(s):  
Cartesian Product ◽  
Topological Properties ◽  
Compatible Topology ◽  
Ternary Semigroup

In this paper, we have discussed various topological properties of (Hausdörff) topological ternary semigroup and topological ternary group. We have proved that the Cartesian product of an arbitrary family of topological ternary semigroups is again a topological ternary semigroup. We have investigated the existence of identity and idempotent in a topological ternary semigroup and discussed a method to topologize a ternary semigroup (group) with a compatible topology using some family of pseudometrics. Finally, we have proved that a compact topological ternary semigroup contains a ternary subgroup.

Stuctures of Ternary Semigroup of Mappings

2020 ◽  
Vol 41 (9) ◽  
pp. 1653-1659
Author(s):  
S. Kar ◽  
I. Dutta ◽  
K. P. Shum
Keyword(s):  
Ternary Semigroup ◽  
Semigroup Of Mappings

A TERNARY SEMIGROUP OF MAPPINGS

1994 ◽  
Vol 27 (3-4) ◽  
pp. 781-792
Author(s):  
Antoni Chronowski
Keyword(s):  
Ternary Semigroup ◽  
Semigroup Of Mappings
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