scholarly journals Computing the Forgotten Topological Index for Zero Divisor Graphs of MV-Algebras

2021 ◽  
pp. 3072-3085
Author(s):  
Necla KIRCALI GÜRSOY
Keyword(s):  
Topological Index ◽  
Zero Divisor ◽  
Mv Algebras

scholarly journals Some results in types of extensions of MV-algebras

2019 ◽  
Vol 105 (119) ◽  
pp. 161-177
Author(s):  
F. Forouzesh ◽  
F. Sajadian ◽  
M. Bedrood
Keyword(s):  
Zero Divisor ◽  
Prime Ideals ◽  
Inverse Topology ◽  
Spectral Topology ◽  
Minimal Prime ◽  
Mv Algebras

We introduce the notions of zero divisor and extension, contraction of ideals in MV-algebras and several interesting types of extensions of MV-algebras. In particular, we show what kinds of extensions MV-algebras will lead in a homeomorphism of the spectral topology and inverse topology on minimal prime ideals. Finally, we investigate the relations among types of extensions of MV-algebras.

The zero-divisor graphs of MV-algebras

2020 ◽  
Vol 24 (8) ◽  
pp. 6059-6068 ◽  
Author(s):  
Aiping Gan ◽  
Yichuan Yang
Keyword(s):  
Zero Divisor ◽  
Mv Algebras

scholarly journals Annihilator graphs of MV-algebras

2020 ◽  
pp. 2150188
Author(s):  
Aiping Gan ◽  
Yichuan Yang
Keyword(s):  
Zero Divisor ◽  
Spanning Subgraph ◽  
Zero Divisor Graph ◽  
Mv Algebra ◽  
Annihilator Graph ◽  
Mv Algebras

In this paper, we introduce the annihilator graph [Formula: see text] of an MV-algebra [Formula: see text]. We show that [Formula: see text] contains the zero-divisor graph [Formula: see text] as a spanning subgraph. We then prove that [Formula: see text] if and only if [Formula: see text]. Moreover, we obtain that the girth [Formula: see text].

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

Semi-simple and complete MV-algebras

1992 ◽  
Vol 29 (1) ◽  
pp. 1-9 ◽  
Author(s):  
L. P. Belluce
Keyword(s):  
Mv Algebras

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 Residuated Structures and Orthomodular Lattices

Studia Logica ◽  
2021 ◽  
Author(s):  
D. Fazio ◽  
A. Ledda ◽  
F. Paoli
Keyword(s):  
Algebraic Logic ◽  
Residuated Lattices ◽  
Quantum Structures ◽  
Heyting Algebras ◽  
Quantum Algebras ◽  
Orthomodular Lattices ◽  
Lattice Of Subvarieties ◽  
Residuated Structures ◽  
Common Framework ◽  
Mv Algebras

AbstractThe variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated $$\ell $$ ℓ -groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated $$\ell $$ ℓ -groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some parts of the theory of join-completions of residuated $$\ell $$ ℓ -groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices.

scholarly journals Priestley duality for MV-algebras and beyond

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wesley Fussner ◽  
Mai Gehrke ◽  
Samuel J. van Gool ◽  
Vincenzo Marra
Keyword(s):  
Large Class ◽  
Order Conditions ◽  
Enriched Environment ◽  
Priestley Duality ◽  
Distributive Lattices ◽  
First Order ◽  
Dual Spaces ◽  
Binary Operations ◽  
New Perspective ◽  
Mv Algebras

Abstract We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions.

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