scholarly journals Boolean Zero Square (BZS) Semigroups

2021 ◽  
Vol 26 (1) ◽  
pp. 31-39
Author(s):  
Pinto G.A.
Keyword(s):  
Inverse Semigroup ◽  
Simple Semigroup ◽  
Sufficient Conditions ◽  
Zero Element ◽  
Necessary And Sufficient Conditions ◽  
Equivalence Relations ◽  
New Class ◽  
Necessary And Sufficient

We introduce a new class of semigroups, that we call BZS - Boolean Zero Square-semigroups. A semigroup S with a zero element, 0, is said to be a BZS semigroup if, for every , we have  or . We obtain some properties that describe the behaviour of the Green’s equivalence relations , ,  and . Necessary and sufficient conditions for a BZS semigroup to be a band and an inverse semigroup are obtained. A characterisation of a special type of BZS completely 0-simple semigroup is presented.

scholarly journals On a topology between Tα and Tγα

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3209-3221
Author(s):  
Dimitrije Andrijevic
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Closure Operators ◽  
New Class ◽  
Necessary And Sufficient

Using the topology T in a topological space (X,T), a new class of generalized open sets called ?-preopen sets, is introduced and studied. This class generates a new topology Tg which is larger than T? and smaller than T??. By means of the corresponding interior and closure operators, among other results, necessary and sufficient conditions are given for Tg to coincide with T? , T? or T??.

scholarly journals Semimodularity and bisimple ω-semigroups

1970 ◽  
Vol 17 (1) ◽  
pp. 79-81 ◽  
Author(s):  
H. E. Scheiblich
Keyword(s):  
Simple Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Primitive Idempotent ◽  
Necessary And Sufficient ◽  
Lattice Of Congruences

Let S be a completely 0-simple semigroup and let Λ(S) be the lattice of congruences on S. G. Lallement (2) has described necessary and sufficient conditions on S for Λ(S) to be modular, and has shown that Λ(S) is always semimodular . This result may be stated: If S is 0-bisimple and contains a primitive idempotent, then Λ(S) is semimodular.

scholarly journals A simplification of D'Alarcao's idempotent separating extensions of inverse semigroups

1978 ◽  
Vol 1 (3) ◽  
pp. 393-396
Author(s):  
Constance C. Edwards
Keyword(s):  
Inverse Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Inverse Semigroups ◽  
Necessary And Sufficient

In [2] D'Alarcao states necessary and sufficient conditions for the attainment of an idempotent-separating extension of an inverse semigroup. To do this D'Alarcao needed essentially three mappings satisfying thirteen conditions. In this paper we show that one can achieve the same results with two mappings satisfying eight conditions.

scholarly journals A unifying approach for some nonexpansiveness conditions on modular vector spaces

2020 ◽  
Vol 25 (5) ◽  
Author(s):  
Andrea Bejenaru ◽  
Mihai Postolache
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Vector Spaces ◽  
Minimizing Sequences ◽  
Ishikawa Iteration ◽  
New Class ◽  
Condition C ◽  
Necessary And Sufficient

This paper provides a new, symmetric, nonexpansiveness condition to extend the classical Suzuki mappings. The newly introduced property is proved to be equivalent to condition (E) on Banach spaces, while it leads to an entirely new class of mappings when going to modular vector spaces; anyhow, it still provides an extension for the modular version of condition (C). In connection with the newly defined nonexpansiveness, some necessary and sufficient conditions for the existence of fixed points are stated and proved. They are based on Mann and Ishikawa iteration procedures, convenient uniform convexities and properly selected minimizing sequences.

Some completely semisimple HNN-extensions of inverse semigroups

2019 ◽  
Vol 30 (02) ◽  
pp. 217-243
Author(s):  
Mohammed Abu Ayyash ◽  
Alessandra Cherubini
Keyword(s):  
Inverse Semigroup ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Inverse Semigroups ◽  
Bicyclic Semigroup ◽  
Hnn Extensions ◽  
Necessary And Sufficient ◽  
Completely Semisimple

We give necessary and sufficient conditions in order that lower bounded HNN-extensions of inverse semigroups and HNN-extensions of finite inverse semigroups are completely semisimple semigroups. Since it is well known that an inverse semigroup is completely semisimple if and only if it does not contain a copy of the bicyclic semigroup, we first characterize such HNN-extensions containing a bicyclic subsemigroup making use of the special feature of their Schützenberger automata.

scholarly journals Relative Infinite Determinacy for Map-Germs

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Changmei Shi ◽  
Donghe Pei
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Target Space ◽  
Equivalence Relations ◽  
Equivalence Group ◽  
Contact Group ◽  
Smooth Map ◽  
Necessary And Sufficient

The infinite determinacy for smooth map-germs with respect to two equivalence relations will be investigated. We treat the space of smooth map-germs with a constraint, and the constraint is that a fixed submanifold in the source space is mapped into another fixed submanifold in the target space. We study the infinite determinacy for such map-germs with respect to a subgroup of right-left equivalence group and finite and infinite determinacy with respect to a subgroup of contact group and give necessary and sufficient conditions for the corresponding determinacy.

Positive fractional 2D continuous-discrete linear systems

2011 ◽  
Vol 59 (4) ◽  
pp. 575-579 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
New Class ◽  
Discrete Linear Systems ◽  
Necessary And Sufficient

Positive fractional 2D continuous-discrete linear systemsA new class of positive fractional 2D continuous-discrete linear systems is introduced. The solution to the equations describing by the new class of systems is derived. Necessary and sufficient conditions for the positivity of the fractional 2D continuous-discrete linear systems are established.

ON A NEW CLASS OF IMPLICATIONS: (g,min)-IMPLICATIONS AND SEVERAL CLASSICAL TAUTOLOGIES

2012 ◽  
Vol 20 (01) ◽  
pp. 1-20 ◽  
Author(s):  
HUA-WEN LIU
Keyword(s):  
Classical Logic ◽  
Functional Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Triangular Norms ◽  
Basic Properties ◽  
New Class ◽  
Fuzzy Implications ◽  
Necessary And Sufficient

A new class of fuzzy implications, called (g, min )-implications, is introduced by means of the additive generators of continuous Archimedean t-conorms, called g-generators. Basic properties of these implications are discussed. It is shown that the (g, min )-implications are really a new class different from the known ( S , N )-, R -, QL - and Yager's f- and g-implications. Generalizations of three classical logic tautologies with implications, viz. law of importation, contraction law and distributivity over triangular norms ( t -norms) and triangular conorms ( t -conorms) are investigated. A series of necessary and sufficient conditions are proposed, under which the corresponding functional equations are satisfied.

scholarly journals On branchwise implicative BCI-algebras

2002 ◽  
Vol 29 (7) ◽  
pp. 417-425 ◽  
Author(s):  
Muhammad Anwar Chaudhry
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
New Class ◽  
Necessary And Sufficient

We introduce a new class of BCI-algebras, namely the class of branchwise implicative BCI-algebras. This class contains the class of implicative BCK-algebras, the class of weakly implicative BCI-algebras (Chaudhry, 1990), and the class of medial BCI-algebras. We investigate necessary and sufficient conditions for two types of BCI-algebras to be branchwise implicative BCI-algebras.

On the Structure of Inverse Semigroup Amalgams

1997 ◽  
Vol 07 (05) ◽  
pp. 577-604 ◽  
Author(s):  
Paul Bennett
Keyword(s):  
Inverse Semigroup ◽  
Free Product ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Inverse Semigroups ◽  
Maximal Subgroups ◽  
Regular Semigroups ◽  
Endomorphism Monoids ◽  
Amalgamated Free Product ◽  
Necessary And Sufficient

This paper is the second of two papers devoted to the study of amalgamated free products of inverse semigroups. We use the characterization of the Schützenberger automata given previously by the author to obtain structural results and preservational properties of lower bounded amalgams. Haataja, Margolis and Meakin have shown that if [S1,S2;U is an amalgam of regular semigroups in which S1∩ S2=U is a full regular subsemigroup of S1 and S2, then the maximal subgroups of the amalgamated free product S1*U S2 may be described by the fundamental groups of certain bipartite graphs of groups. In this paper we show that the maximal subgroups of a lower bounded amalgam [S1,S2;U] are either isomorphic copies of subgroups of S1 and S2 or can be described by the same Bass-Serre theory characterization. It follows, as for the regular case, that if S1 and S2 are combinatorial, then the maximal subgroups of S1*U S2 are free. By studying the endomorphism monoids of the Schützenberger graphs we obtain a number of results concerning when inverse semigroup properties are preserved under the amalgamated free product construction. For example, necessary and sufficient conditions are given for S1*U S2 to be completely semisimple. Under a mild assumption we establish necessary and sufficient conditions for S1*U S2 to have finite ℛ-classes. This enables us to reprove a result of Cherubini, Meakin and Piochi on amalgams of free inverse semigroups. Finally we give sufficient conditions for S1*U S2 to be E-unitary.

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