On the decomposition of prime ideals of ordered semigroups into theirN

1993 ◽  
Vol 47 (1) ◽  
pp. 393-395 ◽  
Author(s):  
Niovi Kehayopulu ◽  
Michael Tsingelis
Keyword(s):  
Prime Ideals ◽  
Ordered Semigroups

On quasi-prime, weakly quasi-prime left ideals in ordered-Γ-semigroups

2010 ◽  
Vol 60 (2) ◽  
Author(s):  
Kostaq Hila
Keyword(s):  
Semigroup Forum ◽  
Prime Ideals ◽  
Ordered Semigroups ◽  
Weakly Prime Ideals

AbstractIn this paper we obtain and establish some important results in ordered Γ-semigroups extending and generalizing those for semigroups given in [PETRICH, M.: Introduction to Semigroups, Merill, Columbus, 1973] and for ordered semigroups from [KEHAYOPULU, N.: On weakly prime ideals of ordered semigroups, Math. Japon. 35 (1990), 1051–1056], [KEHAYOPULU, N.: On prime, weakly prime ideals in ordered semigroups, Semigroup Forum 44 (1992), 341–346] and [XIE, X. Y.—WU, M. F.: On quasi-prime, weakly quasi-prime left ideals in ordered semigroups, PU.M.A. 6 (1995), 105–120]. We introduce and give some characterizations about the quasi-prime and weakly quasi-prime left ideals of ordered-Γ-semigroups. We also introduce the concept of weakly m-systems in ordered Γ-semigroups and give some characterizations of the quasi-prime and weakly quasi-prime left ideals by weakly m-systems.

Ordered semigroups whose elements are separated by prime ideals

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Niovi Kehayopulu
Keyword(s):  
Prime Ideals ◽  
Ordered Semigroups

AbstractIn this paper we add one more characterization of intra-regular ordered semigroups in the existing bibliography by proving that the ordered semigroups whose elements are separated by prime ideals are actually the intra-regular ordered semigroups, a result which generalizes the corresponding result of semigroups (without order).

scholarly journals On f - prime radical in ordered semigroups

2018 ◽  
Vol 16 (1) ◽  
pp. 574-580
Author(s):  
Ze Gu
Keyword(s):  
Prime Radical ◽  
Prime Ideals ◽  
Primary Decomposition ◽  
Ordered Semigroup ◽  
Ordered Semigroups

AbstractIn this paper, we introduce the concepts of f-prime ideals, f-semiprime ideals and f-prime radicals in ordered semigroups. Furthermore, some results on f-prime radicals and f-primary decomposition of an ideal in an ordered semigroup are obtained.

On prime, weakly prime ideals in ordered semigroups

1992 ◽  
Vol 44 (1) ◽  
pp. 341-346 ◽  
Author(s):  
Niovi Kehayopulu
Keyword(s):  
Prime Ideals ◽  
Ordered Semigroups ◽  
Weakly Prime Ideals

scholarly journals On ordered hypersemigroups with idempotent ideals, prime and weakly prime ideals

2018 ◽  
Vol 11 (1) ◽  
pp. 10 ◽  
Author(s):  
Niovi Kehayopulu
Keyword(s):  
Semigroup Forum ◽  
Prime Ideals ◽  
Ordered Semigroups ◽  
A Chain ◽  
Weakly Prime Ideals

Some well known results on ordered semigroups are examined in case of ordered hypersemigroups. Following the paper in Semigroup Forum 44 (1992), 341--346, we prove the following: The ideals of an ordered hypergroupoid$H$ are idempotent if and only if for any two ideals $A$ and $B$ of $H$, we have $A\cap B=(A*B]$. Let now $H$ be an ordered hypersemigroup. Then, the ideals of $H$ are idempotent if and only if $H$ is semisimple. The ideals of $H$ are weakly prime if and only if they are idempotent and they form a chain. The ideals of $H$ are prime if and only if they form a chain and $H$ is intra-regular. The paper serves as an example to show how we pass from ordered semigroups to ordered hypersemigroups.

N-ideals of commutative rings

Filomat ◽  
2017 ◽  
Vol 31 (10) ◽  
pp. 2933-2941 ◽  
Author(s):  
Unsal Tekir ◽  
Suat Koc ◽  
Kursat Oral
Keyword(s):  
Commutative Ring ◽  
Commutative Rings ◽  
Proper Ideal ◽  
Prime Ideals ◽  
Nonzero Identity

In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab ? I with a ? ?0, then b ? I for every a,b ? R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.

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