scholarly journals Regular congruence-preserving extensions of lattices

2001 ◽  
Vol 46 (1) ◽  
pp. 119-130 ◽  
Author(s):  
G. Grätzer ◽  
E. T. Schmidt
Keyword(s):  
Regular Congruence

scholarly journals States and Measures on Hyper BCK-Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xiao-Long Xin ◽  
Pu Wang
Keyword(s):  
Congruence Relation ◽  
Basic Properties ◽  
Mv Algebra ◽  
Regular Congruence ◽  
Bosbach State

We define the notions of Bosbach states and inf-Bosbach states on a bounded hyper BCK-algebra(H,∘,0,e)and derive some basic properties of them. We construct a quotient hyper BCK-algebra via a regular congruence relation. We also define a∘-compatibledregular congruence relationθand aθ-compatibledinf-Bosbach stateson(H,∘,0,e). By inducing an inf-Bosbach states^on the quotient structureH/[0]θ, we show thatH/[0]θis a bounded commutative BCK-algebra which is categorically equivalent to an MV-algebra. In addition, we introduce the notions of hyper measures (states/measure morphisms/state morphisms) on hyper BCK-algebras, and present a relation between hyper state-morphisms and Bosbach states. Then we construct a quotient hyper BCK-algebraH/Ker(m)by a reflexive hyper BCK-idealKer(m). Further, we prove thatH/Ker(m)is a bounded commutative BCK-algebra.

scholarly journals Fuzzy strong regular congruence triples for an E-inversive semigroup

2013 ◽  
Vol 8 ◽  
pp. 675-684
Author(s):  
Yabing Shi ◽  
Zhenji Tian ◽  
Tianjie Zhang
Keyword(s):  
Regular Congruence

The least regular order with respect to a regular congruence on ordered Γ-semigroups

2011 ◽  
Vol 28 (5) ◽  
pp. 975-982
Author(s):  
Manoj Siripitukdet ◽  
Aiyared Iampan
Keyword(s):  
Regular Congruence

scholarly journals REGULAR CONGRUENCES ON AN IDEMPOTENT-REGULAR-SURJECTIVE SEMIGROUP

2013 ◽  
Vol 88 (2) ◽  
pp. 190-196 ◽  
Author(s):  
ROMAN S. GIGOŃ
Keyword(s):  
Equivalence Classes ◽  
Regular Semigroups ◽  
Regular Elements ◽  
Regular Congruence

AbstractA semigroup $S$ is called idempotent-surjective (respectively, regular-surjective) if whenever $\rho $ is a congruence on $S$ and $a\rho $ is idempotent (respectively, regular) in $S/ \rho $, then there is $e\in {E}_{S} \cap a\rho $ (respectively, $r\in \mathrm{Reg} (S)\cap a\rho $), where ${E}_{S} $ (respectively, $\mathrm{Reg} (S)$) denotes the set of all idempotents (respectively, regular elements) of $S$. Moreover, a semigroup $S$ is said to be idempotent-regular-surjective if it is both idempotent-surjective and regular-surjective. We show that any regular congruence on an idempotent-regular-surjective (respectively, regular-surjective) semigroup is uniquely determined by its kernel and trace (respectively, the set of equivalence classes containing idempotents). Finally, we prove that all structurally regular semigroups are idempotent-regular-surjective.

scholarly journals Hyper Homomorphism and Hyper Product of Hyper UP-algebras

2020 ◽  
Vol 13 (3) ◽  
pp. 483-497
Author(s):  
Rohaima M. Amairanto ◽  
Rowena Isla
Keyword(s):  
Congruence Relation ◽  
Regular Congruence

In this paper, we investigate the concept of regular congruence relation on hyper UP-algebras and establish some homomorphism theorems on such algebras. We also examine the notion of hyper product of hyper UP-algebras.

COMPLETE LATTICE HOMOMORPHISM OF STRONGLY REGULAR CONGRUENCES ON -INVERSIVE SEMIGROUPS

2015 ◽  
Vol 100 (2) ◽  
pp. 199-215 ◽  
Author(s):  
XINGKUI FAN ◽  
QIANHUA CHEN ◽  
XIANGJUN KONG
Keyword(s):  
Complete Lattice ◽  
Open Problem ◽  
Lattice Homomorphism ◽  
Regular Semigroups ◽  
Abstract Characterization ◽  
Strongly Regular ◽  
Left And Right ◽  
Regular Congruence

In this paper, we investigate strongly regular congruences on $E$-inversive semigroups $S$. We describe the complete lattice homomorphism of strongly regular congruences, which is a generalization of an open problem of Pastijn and Petrich for regular semigroups. An abstract characterization of left and right traces for strongly regular congruences is given. The strongly regular (sr) congruences on $E$-inversive semigroups $S$ are described by means of certain strongly regular congruence triples $({\it\gamma},K,{\it\delta})$ consisting of certain sr-normal equivalences ${\it\gamma}$ and ${\it\delta}$ on $E(S)$ and a certain sr-normal subset $K$ of $S$. Further, we prove that each strongly regular congruence on $E$-inversive semigroups $S$ is uniquely determined by its associated strongly regular congruence triple.

On Strongly Ordered Congruences and Decompositions of Ordered Semigroups

2008 ◽  
Vol 15 (04) ◽  
pp. 589-598 ◽  
Author(s):  
Xiang-yun Xie
Keyword(s):  
Direct Product ◽  
Subdirect Product ◽  
Ordered Semigroup ◽  
Ordered Semigroups ◽  
Strongly Regular ◽  
Finite Direct Product ◽  
Regular Congruence

In this paper, we introduce the concept of a strongly ordered congruence on a directed ordered semigroup S. We prove that any strongly ordered congruence on S is a strongly regular congruence. We characterize the finite direct product, subdirect product and full subdirect product of ordered semigroups by using the concepts of strongly ordered congruence and regular congruence on an ordered semigroup S.

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