The zero divisor graphs of Boolean posets

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
Vinayak Joshi ◽  
Anagha Khiste
Keyword(s):  
Zero Divisor ◽  
Pseudocomplemented Poset ◽  
Boolean Poset

AbstractIn this paper, it is proved that if B is a Boolean poset and S is a bounded pseudocomplemented poset such that S\Z(S) = {1}, then Γ(B) ≌ Γ(S) if and only if B ≌ S. Further, we characterize the graphs which can be realized as zero divisor graphs of Boolean posets.

scholarly journals Residuated operators in complemented posets

2018 ◽  
Vol 11 (06) ◽  
pp. 1850097 ◽  
Author(s):  
Ivan Chajda ◽  
Helmut Länger
Keyword(s):  
Unary Operation ◽  
Orthomodular Poset ◽  
Orthomodular Lattices ◽  
Orthomodular Posets ◽  
Residuated Poset ◽  
Pseudocomplemented Poset ◽  
Boolean Poset

Using the operators of taking upper and lower cones in a poset with a unary operation, we define operators [Formula: see text] and [Formula: see text] in the sense of multiplication and residuation, respectively, and we show that by using these operators, a general modification of residuation can be introduced. A relatively pseudocomplemented poset can be considered as a prototype of such an operator residuated poset. As main results, we prove that every Boolean poset as well as every pseudo-orthomodular poset can be organized into a (left) operator residuated structure. Some results on pseudo-orthomodular posets are presented which show the analogy to orthomodular lattices and orthomodular posets.

THE CYLINDRICAL CROSSING NUMBER OF ZERO DIVISOR GRAPHS

2020 ◽  
Vol 9 (8) ◽  
pp. 5901-5908
Author(s):  
M. Sagaya Nathan ◽  
J. Ravi Sankar
Keyword(s):  
Zero Divisor ◽  
Crossing Number

Eigenvalues of zero divisor graphs of principal ideal rings

2021 ◽  
pp. 1-15
Author(s):  
Jitsupat Rattanakangwanwong ◽  
Yotsanan Meemark
Keyword(s):  
Principal Ideal ◽  
Zero Divisor

scholarly journals Correction to: Classification of non-local rings with genus two zero-divisor graphs

2021 ◽  
Vol 25 (4) ◽  
pp. 3355-3356
Author(s):  
T. Asir ◽  
K. Mano ◽  
T. Tamizh Chelvam
Keyword(s):  
Zero Divisor ◽  
Local Rings ◽  
Non Local ◽  
Genus Two

scholarly journals Algebras Describing Pseudocomplemented, Relatively Pseudocomplemented and Sectionally Pseudocomplemented Posets

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 753
Author(s):  
Ivan Chajda ◽  
Helmut Länger
Keyword(s):  
Universal Algebra ◽  
Relational Structures ◽  
Pseudocomplemented Poset ◽  
The Given ◽  
The Relationship ◽  
Congruence Properties

In order to be able to use methods of universal algebra for investigating posets, we assigned to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset, a certain algebra (based on a commutative directoid or on a λ-lattice) which satisfies certain identities and implications. We show that the assigned algebras fully characterize the given corresponding posets. A certain kind of symmetry can be seen in the relationship between the classes of mentioned posets and the classes of directoids and λ-lattices representing these relational structures. As we show in the paper, this relationship is fully symmetric. Our results show that the assigned algebras satisfy strong congruence properties which can be transferred back to the posets. We also mention applications of such posets in certain non-classical logics.

scholarly journals On the set of divisors with zero geometric defect

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh Tuan Huynh ◽  
Duc-Viet Vu
Keyword(s):  
Line Bundle ◽  
Zero Divisor ◽  
Ample Line Bundle ◽  
Holomorphic Section ◽  
Projective Manifold ◽  
Holomorphic Curve ◽  
Very Ample Line Bundle ◽  
Complex Projective ◽  
Geometric Defect

AbstractLet {f:\mathbb{C}\to X} be a transcendental holomorphic curve into a complex projective manifold X. Let L be a very ample line bundle on {X.} Let s be a very generic holomorphic section of L and D the zero divisor given by {s.} We prove that the geometric defect of D (defect of truncation 1) with respect to f is zero. We also prove that f almost misses general enough analytic subsets on X of codimension 2.

scholarly journals Sub-semigroups determined by the zero-divisor graph

2008 ◽  
Vol 308 (22) ◽  
pp. 5122-5135 ◽  
Author(s):  
Tongsuo Wu ◽  
Dancheng Lu
Keyword(s):  
Zero Divisor ◽  
Zero Divisor Graph

Planar zero divisor graphs of partially ordered sets

2012 ◽  
Vol 137 (1-2) ◽  
pp. 27-35 ◽  
Author(s):  
M. Afkhami ◽  
Z. Barati ◽  
K. Khashyarmanesh
Keyword(s):  
Zero Divisor ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered
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