Add to ORKGThe ideal extensions of semigroups—without order—have been first considered by Clifford (1950). In this paper, we give the main theorem of the ideal extensions for ordered sets. If P, Q are disjoint ordered sets, we construct (all) the ordered sets V which have an ideal P ′ which is isomorphic to P, and the complement of P ′ in V is isomorphic toQ. Conversely, we prove that every extension of an ordered set P by an ordered set Q can be so constructed. Illustrative examples of the main theorem in case of finite ordered sets are given. 2000 Mathematics Subject Classification: 06A06
In this paper, we introduce the notion of k-ideal, m−k ideal, prime ideal, maximal ideal, filter, ir...
It is known that in a commutative ring with identity element any maximal ideal is prime. Similar res...
In this paper we characterize both the Clifford and left Clifford ordered semigroups by their bi-ide...
AbstractThe aim of this paper is to study semigroups with the ideal extension property. We establish...
Ideals of ordered groupoids were defined by second author in [2]. Considering the question under wha...
Ideals of ordered groupoids were defined by second author in [2]. Considering the question under wha...
Ideals of ordered groupoids were defined by second author in [2]. Considering the question under wha...
Ideals of ordered groupoids were defined by second author in [2]. Considering the question under wha...
The notion of Γ-semigroups was introduced by Sen in 1981. The concept of Γ-semigroups is a generaliz...
Exactly as in semigroups, Green’s relations play an important role in the theory of ordered semigrou...
Abstract. The notion of a Γ-semigroup was introduced by Sen [8] in 1981. We can see that any semigro...
AbstractBy finding invariant embeddings of a partially ordered set X into the semigroups it is shown...
The uni-soft type of bi-ideals in ordered semigroup is considered. The notion of a uni-soft bi-ideal...
In this paper we characterize both the Clifford and left Clifford ordered semigroups by their bi-ide...
Exactly as in semigroups, Green's relations play an important role in the theory of ordered semigrou...
In this paper, we introduce the notion of k-ideal, m−k ideal, prime ideal, maximal ideal, filter, ir...
It is known that in a commutative ring with identity element any maximal ideal is prime. Similar res...
In this paper we characterize both the Clifford and left Clifford ordered semigroups by their bi-ide...
AbstractThe aim of this paper is to study semigroups with the ideal extension property. We establish...
Ideals of ordered groupoids were defined by second author in [2]. Considering the question under wha...
Ideals of ordered groupoids were defined by second author in [2]. Considering the question under wha...
Ideals of ordered groupoids were defined by second author in [2]. Considering the question under wha...
Ideals of ordered groupoids were defined by second author in [2]. Considering the question under wha...
The notion of Γ-semigroups was introduced by Sen in 1981. The concept of Γ-semigroups is a generaliz...
Exactly as in semigroups, Green’s relations play an important role in the theory of ordered semigrou...
Abstract. The notion of a Γ-semigroup was introduced by Sen [8] in 1981. We can see that any semigro...
AbstractBy finding invariant embeddings of a partially ordered set X into the semigroups it is shown...
The uni-soft type of bi-ideals in ordered semigroup is considered. The notion of a uni-soft bi-ideal...
In this paper we characterize both the Clifford and left Clifford ordered semigroups by their bi-ide...
Exactly as in semigroups, Green's relations play an important role in the theory of ordered semigrou...
In this paper, we introduce the notion of k-ideal, m−k ideal, prime ideal, maximal ideal, filter, ir...
It is known that in a commutative ring with identity element any maximal ideal is prime. Similar res...
In this paper we characterize both the Clifford and left Clifford ordered semigroups by their bi-ide...