Galois theory for clones and superclones

2016 ◽  
Vol 26 (4) ◽  
Author(s):  
Nikolay A. Peryazev ◽  
Ivan K. Sharankhaev
Keyword(s):  
Galois Theory ◽  
Galois Connection ◽  
Finite Sets ◽  
Closed Sets ◽  
Equation Solvability

AbstractWe study clones (closed sets of operations that contain projections) and superclones on finite sets. According to A. I. Mal’tsev a clone may be considered as an algebra. If we replace algebra universe with a set of multioperations and add the operation of simplest equation solvability then we will obtain an algebra called a superclone. The paper establishes Galois connection between clones and superclones.

scholarly journals An Invitation to Model-Theoretic Galois Theory

2010 ◽  
Vol 16 (2) ◽  
pp. 261-269 ◽  
Author(s):  
Alice Medvedev ◽  
Ramin Takloo-Bighash
Keyword(s):  
Galois Group ◽  
Galois Theory ◽  
Order Theory ◽  
Closed Field ◽  
Finite Sets ◽  
Algebraically Closed Field ◽  
First Order ◽  
First Order Theory ◽  
Special Case ◽  
Large Model

AbstractWe carry out some of Galois' work in the setting of an arbitrary first-order theory T. We replace the ambient algebraically closed field by a large model M of T, replace fields by definably closed subsets of M, assume that T codes finite sets, and obtain the fundamental duality of Galois theory matching subgroups of the Galois group of L over F with intermediate extensions F ≤ K ≤ L. This exposition of a special case of [10] has the advantage of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorphisms.

Field Extensions and Galois Theory

1984 ◽  
Author(s):  
Julio R. Bastida ◽  
Roger Lyndon
Keyword(s):  
Galois Theory ◽  
Field Extensions

Generalized ʎ-Closed Sets and (ʎ-ʏ)*-Continuous Function

2017 ◽  
Vol 4 (ICBS Conference) ◽  
pp. 1-17 ◽  
Author(s):  
Alias Khalaf ◽  
Sarhad Nami
Keyword(s):  
Continuous Function ◽  
Closed Sets

ON ir-CLOSED SETS IN TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (5) ◽  
pp. 2573-2582
Author(s):  
A. M. Anto ◽  
G. S. Rekha ◽  
M. Mallayya
Keyword(s):  
Topological Spaces ◽  
Closed Sets

ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (11) ◽  
pp. 9353-9360
Author(s):  
G. Selvi ◽  
I. Rajasekaran
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Open Set ◽  
Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

ON CONTRA SOFT ARS CLOSED SETS IN SOFT TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (3) ◽  
pp. 921-926
Author(s):  
P. Anbarasi Rodrigo ◽  
K. Rajendra Suba
Keyword(s):  
Topological Spaces ◽  
Closed Sets

FUZZY MAXIMAL, MINIMAL OPEN AND CLOSED SETS

2020 ◽  
Vol 9 (10) ◽  
pp. 7741-7747
Author(s):  
A. Swaminathan ◽  
S. Sivaraja
Keyword(s):  
Closed Sets
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