Lau D. — Function Algebras on Finite Sets :: Электронная библиотека попечительского совета мехмата МГУ

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Lau D. — Function Algebras on Finite Sets

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Название: Function Algebras on Finite Sets

Автор: Lau D.

Аннотация:

Functions which are defined on finite sets occur in almost all fields of mathematics. For more than 80 years algebras whose universes are such functions (so-called function algebras), have been intensively studied.

This book gives a broad introduction to the theory of function algebras and leads to the cutting edge of research. To familiarize the reader from the very beginning on with the algebraic side of function algebras the more general concepts of the Universal Algebra is given in the first part of the book. The second part on fuction algebras covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, clone theory.

This book is an insdispensible source on function algebras for graduate students and researchers in mathematical logic and theoretical computer science.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2006

Количество страниц: 688

Добавлена в каталог: 10.05.2008

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Предметный указатель

A.I. Mal’tsev’s theorem      268
Adding of certain fictitious variables      94
Adding of fictitious coordinates (rows)      129
Algebra      26
Algebra of finite type      27
Algebra, axiom of      27
Algebra, closed subset      32
Algebra, demiprimal      104
Algebra, demisemiprimal      104
Algebra, directly irreducible      64
Algebra, extension of      31
Algebra, factor      55
Algebra, finite      26
Algebra, finitely axiomatizable      84
Algebra, finitely based      84
Algebra, free      79
Algebra, fundamental operations      26
Algebra, generating system      32
Algebra, hemiprimal      104
Algebra, infinite      26
Algebra, infraprimal      104
Algebra, partial      26
Algebra, preprimal      104
Algebra, primal      104
Algebra, quasiprimal      104
Algebra, quotient      55
Algebra, semiprimal      104
Algebra, set of all subalgebras      33
Algebra, simple      53
Algebra, subalgebra      31
Algebra, type      26 73
Algebra, universal      26
Algebra, universe      26
Algebras of same type      27
All relation      43
All-congruence      see “Congruence”
Antiisomorphic      59
Antiisomorphism      59
Arity      see “Operation”
Arity congruence      235
atom      112
Atomic proposition      106
Automorphism      52
Automorphism, inner      285
Basis      98
Block      44
Boolean algebra      30
Cartesian product      64
Chain      36
Characterization theorem for Sheffer- functions      215
class      97
Class of algebras, closed      72
Class of all models of $\Sigma$       77
Class of type $\mathfrak{B}$       174
Class of type $\mathfrak{C}$       173
Class of type $\mathfrak{L}$       171
Class of type $\mathfrak{M}$       165
Class of type $\mathfrak{U}$       170
Class of type $\mathfrak{X}$       165
Class, B-projectable      337
Class, inverse image      337
Class, l-class      280
Class, maximal      98
Class, minimal      589
Class, order      98
Class, submaximal      98
Clone      97
Clone, minimal      590
Clone, strong      599
Closed set system      45
Closure      97
Closure operator      45
Closure operator, algebraic      46
Closure, deductive      82
Co-class      141
Co-clone      127
Co-group      138
Co-monoid      138
complete      98
Completeness criterion for       156
Completeness criterion for       191
Completeness criterion for $P_{k,l}$       352
Completeness criterion for       501
Completeness criterion for the class of all idempotent functions of       501
Completeness problem      117
Completeness theorem for the equational logic      84
Completeness theorem of proportional logic      110
composition      25
Composition, general      129
Conclusion      77
Congruence      52 234
Congruence of the first kind      235
Congruence of the second kind      235
Congruence relation      see “Congruence”
Congruence theorem for       237
Congruence, congruence class      55
Congruence, fully invariant      83
Congruence, n-congruence      279
Congruence, theorem for maximal clones      265
Congruence, trivial      53 234
Constant      93
Countability criterion      221
Cyclical exchanging of the lines      127
Deductive closure      82
Depth of a subclass      433
Diagonal      126
Diagonale      43
DIMENSION      291
Direct product      61
Direct product of classes      397
Direct product of functions      397
DNF      99
Domain      see “Operation”
Doubling of coordinates (rows)      129
Dual isomorphic      59
Duality principle of the lattice theory      36
Element, central      174
Element, greatest      165
Element, inverse      28
Element, least      165
Element, neutral      28
Elementary operations      95
Embedding      67
Endomorphism      52
equation      76
Equational class      77
Equational theory      77
Equivalence class      43
Equivalence relation      42
Equivalence relation, equivalence class      43
Equivalence relation, finer      351
Equivalence relation, permutable      62
Equivalence relation, transversal to s      556
Equivalence relation, trivial      43
Exchange of the first two rows      127
Factor algebra      55
Factor set      43
Family of sets      65
Fictitious place of a function      93
Field      29
Floor function      331
Free algebra      79
Free generating set      79
Function algebra      30
Function algebra, full      96
Function algebra, iterative full      96
Function, autoduale      167
Function, boolean      93
Function, component      371
Function, components of f      359

Function, constant      93
Function, extended      600
Function, linear      171
Function, monotone      165
Function, n-ary on A      91
Function, near unanimity function      342
Function, partial      598
Function, preserves the relation $\rho$       130
Function, quasi-linear      171
Function, quasilinear      456
Function, r-th component      168
Function, reducible      150
Function, reduction      599
Function, restricted      600
Function, semiprojection      591
Function, subfunction      598
Function, total      598
Functions, $\kappa$ -congruent      234
Functions, are associated      238
Functions, identity of      93
Fundamental group      218
Fundamental lemma of Jablonskij      102
Fundamental operations      see “Algebra”
Fundamental semigroup      218
Fundamental set      218
Fuzzy logic      116
Galois connection      59
Galois correspondence      59
Generating set      48
Generating system      48 98
Gorlov’s tqheorem      281
Graphic, n-teof A      133
Group      28
Group, abelian      28
Group, additive notation      28
Group, commutative      28
Group, semiregular representation      557
Gruppoid      27
Haddad — Rosenberg theorem      616
Hasse diagram      36
Hilbert-type-calculus      107
Homomorphism      51
Homomorphism theorem for groups      57
Homomorphism theorem for rings      58
Homomorphism theorem, general      55
Homomorphism, kernel      52
Homomorphism, natural      55
Homomorphism, quotient      55
Hull      45 97
Hull system      45
I.A. Mal’tsev’s theorem      241
Ideal      58
Identification of certain variables of f      94
Identification of coordinates      129
Identity      43 76
Inductively set system      68
Information transformer      116
Intersection      127
Inverse element      28
Inverse image, homomorphic      174
Isomorphic      39
Isomorphic lattices      39
Isomorphism      39 52
Isomorphism, anti-      59
Isomorphism, dual      59
Kernel of a group homomorphism      57
Kernel of a homomorphism      52
Kernel of a ring homomorphism      58
Krasner-algebra of first kind      138
Krasner-algebra of second kind      138
Lattice      30
Lattice with 0 and 1      30
Lattice, bounded      30
Lattice, complete      42
Lattice, distributive      30
Lattice, first definition      35
Lattice, isomorphic      39
Lattice, second definition      37
Lattice, sublattice      41
Left unit      241
Lexicographical order      132
Limit class      280
Main theorem of the equational theory, first      81
Main theorem of the equational theory, second      84
Majority function      591
Maltsev-operations      31 95
Mapping, homomorphic      51
Mapping, isomorphic      52
Mapping, order-preserving      39
Mapping, projection-      61
Minority function      591
Module      29
Module, over a unitary ring      29
Module, over the ring $\mathbb{R}$       29
Module, R-module      29
modus ponens      108
Monoid      28
Neutral element      28
Normal form, disjunctive      99
Normal subgroup      56
Operation symbol      73
Operation, arity      25
Operation, domain      25
Operation, elementary on       127
Operation, n-ary partial      25
Operation, nullary      25
Operation, range      25
Order      98
Order diagram      36
Order, dual      59
Order, partial      36
Partition      44
Peirce decomposition      397
Permutation of coordinates      128
Permutation of variables of f      94
Polymorphism      130
POSET      36
Poset, antiisomorphic      59
Poset, complete      41
Poset, dual isomorphic      59
Post’s theorem      148
Predecessor, proper      292
Predicate      111
Preserve, a relation pair      140
Preserving of a set      97
Preserving of relations      130
Product, cartesian      127
Projection      93
Projection mapping      see “Mapping”
Projection onto the $\alpha_1$ -te, ..., $\alpha_t$ -te coordinates      128
Projection onto the i-th coordinate      127
Proposition      105
Quotient algebra      55
RANGE      see “Operation”
Reduct of an algebra      104
Relation algebra on       127
Relation algebra on , full      127
Relation degree      291
Relation pair      140
Relation pairalgebra, full      141
Relation product      129
Relation set, $\alpha$ -permissible      350
Relation set, $\rho$ -independent      179
Relation set, h-regular      178
Relation set, is closed      127
Relation set, minimal coarsening      351
Relation set, permissible      350
Relation, $\rho$ -derivable      127 499 515
Relation, $\theta_s$ -closed      555
Relation, ${\zeta, \tau, pr,\wedge, \times}$ -derivable      128

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