scholarly journals On refined generalised quasi-adequate transversals

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 299-313
Author(s):  
Xiangjun Kong ◽  
Pei Wang
Keyword(s):  
Structure Theorem ◽  
Interesting Property ◽  
Product Structure ◽  
Abundant Semigroup ◽  
Property A ◽  
The Real ◽  
Spined Product ◽  
Abundant Semigroups

Some properties and characterizations for abundant semigroups with generalised quasiadequate transversals are explored. In such semigroups, an interesting property [?a,b ? Re1S, VSo(a) ? VSo (b) ? 0 ? VSo (a) = VSo (b)] is investigated and thus the concept of refined generalised quasi-adequate transversals, for short, RGQA transversals is introduced. It is shown that RGQA transversals are the real common generalisations of both orthodox transversals and adequate transversals in the abundant case. Finally, by means of two abundant semigroups R and L, a spined product structure theorem for an abundant semigroup with a quasi-ideal RGQA transversal is established.

scholarly journals Quasi-ideal Ehresmann transversals: The spined product structure

2021 ◽  
Vol 19 (1) ◽  
pp. 77-86
Author(s):  
Xiangjun Kong ◽  
Pei Wang ◽  
Jian Tang
Keyword(s):  
Structure Theorem ◽  
Product Structure ◽  
Abundant Semigroup ◽  
Spined Product ◽  
Equivalent Conditions

Abstract In any U-abundant semigroup with an Ehresmann transversal, two significant components R and L are introduced in this paper and described by Green’s ∼ \sim -relations. Some interesting properties associated with R and L are explored and some equivalent conditions for the Ehresmann transversal to be a quasi-ideal are acquired. Finally, a spined product structure theorem is established for a U-abundant semigroup with a quasi-ideal Ehresmann transversal by means of R and L.

On Uσ-Abundant Semigroups

2012 ◽  
Vol 19 (01) ◽  
pp. 41-52 ◽  
Author(s):  
Xueming Ren ◽  
Qingyan Yin ◽  
K. P. Shum
Keyword(s):  
Structure Theorem ◽  
Abundant Semigroup ◽  
Regular Semigroups ◽  
Permutation Identity ◽  
Spined Product ◽  
Abundant Semigroups ◽  
The Relationship ◽  
Ehresmann Semigroups

A U-abundant semigroup whose subset U satisfies a permutation identity is said to be Uσ-abundant. In this paper, we consider the minimum Ehresmann congruence δ on a Uσ-abundant semigroup and explore the relationship between the category of Uσ-abundant semigroups (S,U) and the category of Ehresmann semigroups (S,U)/δ. We also establish a structure theorem of Uσ-abundant semigroups by using the concept of quasi-spined product of semigroups. This generalizes a result of Yamada for regular semigroups in 1967 and a result of Guo for abundant semigroups in 1997.

scholarly journals The characterization and the product of quasi-Ehresmann transversals

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 2051-2060
Author(s):  
Xiangjun Kong ◽  
Pei Wang
Keyword(s):  
Abundant Semigroup ◽  
Regular Semigroups ◽  
The Real ◽  
Abundant Semigroups

Wang (Filomat 29(5), 985-1005, 2015) introduced and investigated quasi-Ehresmann transversals of semi-abundant semigroups satisfy conditions (CR) and (CL) as the generalizations of orthodox transversals of regular semigroups in the semi-abundant case. In this paper, we give two characterizations for a generalized quasi-Ehresmann transversal to be a quasi-Ehresmann transversal. These results further demonstrate that quasi-Ehresmann transversals are the ?real? generalizations of orthodox transversals in the semi-abundant case. Moreover, we obtain the main result that the product of any two quasi-ideal quasi-Ehresmann transversals of a semi-abundant semigroup S which satisfy the certain conditions is a quasi-ideal quasi-Ehresmann transversal of S.

A Structure Theorem of Regular ${\cal H}^\sharp$-Cryptographs

2008 ◽  
Vol 15 (04) ◽  
pp. 653-666 ◽  
Author(s):  
Xiangzhi Kong ◽  
Zhiling Yuan ◽  
K. P. Shum
Keyword(s):  
Structure Theorem ◽  
Abundant Semigroup ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Abundant Semigroups ◽  
Completely Regular Semigroups ◽  
Semilattice Of Semigroups ◽  
Strong Semilattice ◽  
Green Relations ◽  
Strong Semilattice Of Semigroups

A new set of generalized Green relations is given in studying the [Formula: see text]-abundant semigroups. By using the generalized strong semilattice of semigroups recently developed by the authors, we show that an [Formula: see text]-abundant semigroup is a regular [Formula: see text]-cryptograph if and only if it is an [Formula: see text]-strong semilattice of completely [Formula: see text]-simple semigroups. This result not only extends the well known result of Petrich and Reilly from the class of completely regular semigroups to the class of semiabundant semigroups, but also generalizes a well known result of Fountain on superabundant semigroups from the class of abundant semigroups to the class of semiabundant semigroups.

scholarly journals Semi-abundant semigroups with quasi-Ehresmann transversals

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 985-1005
Author(s):  
Shoufeng Wang
Keyword(s):  
Structure Theorem ◽  
Regular Semigroups ◽  
Abundant Semigroups

Chen (Communications in Algebra 27(2), 4275-4288, 1999) introduced and investigated orthodox transversals of regular semigroups. In this paper, we initiate the investigation of quasi-Ehresmann transversals of semi-abundant semigroups which are generalizations of orthodox transversals of regular semigroups. Some interesting properties associated with quasi-Ehresmann transversals are established. Moreover, a structure theorem of semi-abundant semigroups with generalized bi-ideal strong quasi-Ehresmann transversals is obtained. Our results generalize and enrich Chen?s results.

scholarly journals On Naturally Ordered Abundant Semigroups with an Adequate Monoid Transversal

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Wei Chen
Keyword(s):  
Structure Theorem ◽  
Abundant Semigroups

In this paper, we study a class of naturally ordered abundant semigroups with an adequate monoid transversal, namely, naturally ordered concordant semigroups with an adequate monoid transversal. After giving some properties of such semigroups, we obtain a structure theorem for naturally ordered concordant semigroups with an adequate monoid transversal.

scholarly journals Deniable Key Establishment Resistance against eKCI Attacks

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Łukasz Krzywiecki ◽  
Tomasz Wlisłocki
Keyword(s):  
Authentication Protocol ◽  
The Other ◽  
Property A ◽  
Key Establishment ◽  
The Real ◽  
Protocol Execution ◽  
Key Compromise Impersonation

In extended Key Compromise Impersonation (eKCI) attack against authenticated key establishment (AKE) protocols the adversary impersonates one party, having the long term key and the ephemeral key of the other peer party. Such an attack can be mounted against variety of AKE protocols, including 3-pass HMQV. An intuitive countermeasure, based on BLS (Boneh–Lynn–Shacham) signatures, for strengthening HMQV was proposed in literature. The original HMQV protocol fulfills the deniability property: a party can deny its participation in the protocol execution, as the peer party can create a fake protocol transcript indistinguishable from the real one. Unfortunately, the modified BLS based version of HMQV is not deniable. In this paper we propose a method for converting HMQV (and similar AKE protocols) into a protocol resistant to eKCI attacks but without losing the original deniability property. For that purpose, instead of the undeniable BLS, we use a modification of Schnorr authentication protocol, which is deniable and immune to ephemeral key leakages.

scholarly journals The product of quasi-ideal refined generalised quasi-adequate transversals

2019 ◽  
Vol 17 (1) ◽  
pp. 43-51
Author(s):  
Xiangjun Kong ◽  
Pei Wang ◽  
Yonghong Wu
Keyword(s):  
Regularity Condition ◽  
Rectangular Band ◽  
Abundant Semigroup ◽  
The Real ◽  
Adequate Transversal

Abstract As the real common generalisations of both orthodox transversals and adequate transversals in the abundant case, the concept of refined generalised quasi-adequate transversal, for short, RGQA transversal was introduced by Kong and Wang. In this paper, an interesting characterization for a generalised quasi-adequate transversal to be refined is acquired. It is shown that the product of every two quasi-ideal RGQA transversals of the abundant semigroup S satisfying the regularity condition is a quasi-ideal RGQA transversal of S and that all quasi-ideal RGQA transversals of S compose a rectangular band. The related results concerning adequate transversals are generalised and enriched.

scholarly journals Self-injectivity of semigroup algebras

2020 ◽  
Vol 18 (1) ◽  
pp. 333-352
Author(s):  
Junying Guo ◽  
Xiaojiang Guo
Keyword(s):  
Regular Semigroup ◽  
Necessary Conditions ◽  
Semigroup Algebra ◽  
Semigroup Algebras ◽  
Abundant Semigroup ◽  
Regular Semigroups ◽  
Abundant Semigroups ◽  
Sufficient And Necessary Conditions ◽  
Finite Regular Semigroup

Abstract It is proved that for an IC abundant semigroup (a primitive abundant semigroup; a primitively semisimple semigroup) S and a field K, if K 0[S] is right (left) self-injective, then S is a finite regular semigroup. This extends and enriches the related results of Okniński on self-injective algebras of regular semigroups, and affirmatively answers Okniński’s problem: does that a semigroup algebra K[S] is a right (respectively, left) self-injective imply that S is finite? (Semigroup Algebras, Marcel Dekker, 1990), for IC abundant semigroups (primitively semisimple semigroups; primitive abundant semigroups). Moreover, we determine the structure of K 0[S] being right (left) self-injective when K 0[S] has a unity. As their applications, we determine some sufficient and necessary conditions for the algebra of an IC abundant semigroup (a primitively semisimple semigroup; a primitive abundant semigroup) over a field to be semisimple.

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