On Exchange QB∞-Rings

2007 ◽  
Vol 14 (04) ◽  
pp. 613-623 ◽  
Author(s):  
Huanyin Chen
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Exchange Ring ◽  
New Class ◽  
Necessary And Sufficient ◽  
Invertible Matrices ◽  
Diagonal Reduction ◽  
Square Matrix

In this paper, we introduce a new class of rings, the QB∞-rings. We investigate necessary and sufficient conditions under which an exchange ring is a QB∞-ring. The modules over an exchange QB∞-ring are studied. Also, we prove that every regular square matrix over an exchange QB∞-ring admits a diagonal reduction by pseudo-invertible matrices.

EXCHANGE RINGS OVER WHICH EVERY REGULAR MATRIX ADMITS DIAGONAL REDUCTION

2004 ◽  
Vol 03 (02) ◽  
pp. 207-217 ◽  
Author(s):  
HUANYIN CHEN
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Exchange Ring ◽  
Regular Matrix ◽  
Finitely Generated ◽  
Exchange Rings ◽  
Necessary And Sufficient ◽  
Diagonal Reduction

In this paper, we investigate the necessary and sufficient conditions on exchange rings, under which every regular matrix admits diagonal reduction. Also we show that an exchange ring R is strongly separative if and only if for any finitely generated projective right R-module C, if A and B are any right R-modules such that 2C⊕A≅C⊕B, then C⊕A≅B.

On Exchange Hermitian Rings

2010 ◽  
Vol 17 (01) ◽  
pp. 87-100 ◽  
Author(s):  
Huanyin Chen
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Exchange Ring ◽  
Regular Matrix ◽  
Exchange Rings ◽  
Necessary And Sufficient ◽  
Diagonal Reduction

In this article, we investigate new necessary and sufficient conditions on an exchange ring under which every regular matrix admits a diagonal reduction. We prove that an exchange ring R is an hermitian ring if and only if for any n ≥ 2 and any regular x ∈ Rn, there exists u ∈ CLn(R) such that x = xux; if and only if for any n ≥ 2 and any regular x ∈ Rn, there exists u ∈ CLn(R) such that xu ∈ R is an idempotent. Furthermore, we characterize such exchange rings by means of reflexive inverses and n-pseudo-similarity.

scholarly journals On circulant codes with prescribed distances

1977 ◽  
Vol 16 (3) ◽  
pp. 361-369
Author(s):  
M. Deza ◽  
Peter Eades
Keyword(s):  
Sufficient Conditions ◽  
Difference Sets ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Weighing Matrices ◽  
Cyclic Difference Sets ◽  
The Matrix ◽  
Circulant Codes ◽  
Necessary And Sufficient ◽  
Square Matrix

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.

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 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.

scholarly journals Transposable and symmetrizable matrices

1980 ◽  
Vol 29 (4) ◽  
pp. 469-474 ◽  
Author(s):  
David McCarthy ◽  
Brendan D. McKay
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Permutation Matrix ◽  
Permutation Matrices ◽  
Symmetrizable Matrices ◽  
Necessary And Sufficient ◽  
Square Matrix

AbstractA square matrix A is transposable if P(RA) = (RA)T for some permutation matrices p and R, and symmetrizable if (SA)T = SA for some permutation matrix S. In this paper we find necessary and sufficient conditions on a permutation matrix P so that A is always symmetrizable if P(RA) = (RA)T for some permutation matrix R.

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.

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.

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