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The set of types of a finitely generated variety

Joel D. Berman, Emil W. Kiss, Péter Prőhle, Ágnes Szendrei
1993 Discrete Mathematics  
Priihle and A. Szendrei, The set of types of a finitely generated variety, Discrete Mathematics 112 (1993) l-20.  ...  The set of types qf a,finitely generuted aarietv  ...  Thenfg(T)+ T and (f(a),f(b))=(fg(c),fg(d))m(T). 0 The set of types of a finitely generated variety I Two special instances of this description of a(a, b) are contained in the next lemma.  ... 
doi:10.1016/0012-365x(93)90219-j fatcat:5s67pgrodrevhmrcxhfwoflr6y

Page 1797 of Mathematical Reviews Vol. , Issue 93d [page]

1993 Mathematical Reviews  
The set of types that appear is called the type set of the algebra, and the type set of a locally finite variety is the union of the type sets of the finite algebras in the variety. The author and R.  ...  Szendrei and the reviewer have given a polynomial-time algorithm to compute the type set of a finite algebra [“The set of types of a finitely generated variety”, Discrete Math., to appear].  ... 

Finiteness of non-constant maps over number fields [article]

Ariyan Javanpeykar
2021 arXiv   pre-print
Motivated by the intermediate Lang conjectures on hyperbolicity and rational points, we prove new finiteness results for non-constant morphisms from a fixed variety to a fixed variety defined over a number  ...  field by applying Faltings's finiteness results to moduli spaces of maps.  ...  If X is a projective variety of general type over k and Y is a projective variety over k, then the set of dominant rational maps Y 99K X is finite. We now prove our first technical result.  ... 
arXiv:2112.11408v1 fatcat:hsjcfifienartmjbj4r5rheygu

An Introduction to Tame Congruence Theory [chapter]

Emil W. Kiss
1997 Algebraic Model Theory  
The aim of this paper is to give a non-technical introduction to this topic for people having a general background in mathematics.  ...  These are models having no relation symbols, and so are given by an underlying set, and a system of finitary basic operations.  ...  Hobby) Let A be a finite algebra such that the types 1 and 5 do not occur in the finite members of the variety V generated by A.  ... 
doi:10.1007/978-94-015-8923-9_5 fatcat:x5avartgknhn7lnpdxzg3bj6zq

A field guide to equational logic

George F. McNulty
1992 Journal of symbolic computation  
By way of this relation each equational theory-that is, each set of equations closed under logical consequence-is associated with a variety of algebras : the class of all algebras in which each equation  ...  The concept of a ring is ordinarily presented by saying that a ring is a system (R, +, -, , 0,1) in which the following equations are true : A ring is an algebra-meaning here a nonempty set endowed with  ...  We will say a property P of finite sets of equations of similarity type o is decidable iff the set {E : E is a finite set of equations of type v which has P} is recursive .  ... 
doi:10.1016/0747-7171(92)90013-t fatcat:ou4teabieffhhlciea4odb546i

On locally finite varieties with undecidable equational theory

Marcel Jackson
2002 Algebra Universalis  
A second kind of example presented in the above papers are varieties V in which every finitely generated V-free algebra has a decidable word problem but the equational theory of V is undecidable.  ...  variety of groups (of type 2, 1, 0 ).  ...  We now attempt to encapsulate the method referred to above. Let V be a variety of type F and Id (V) be the set of identities of V in some fixed countably infinite set of variables X.  ... 
doi:10.1007/s00012-002-8169-0 fatcat:povjkwr22ncaha7ofidvtew42e

Page 60 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
Two finite resets P and Q of the same type generate the same relation variety iff P and Q have up to isomorphisms the same minimal resets.  ...  Any such map o then extends to a map @ on the set of all terms of type t. The set Hyp(rt) of all hypersubstitutions of type t forms a monoid under a composition operation.  ... 

Belyi's theorem for complete intersections of general type [article]

Ariyan Javanpeykar
2016 arXiv   pre-print
Our proof uses the higher-dimensional analogue of the Shafarevich boundedness conjecture for families of canonically polarized varieties, finiteness results for maps to varieties of general type, and rigidity  ...  We give a Belyi-type characterisation of smooth complete intersections of general type over C which can be defined over Q̅.  ...  We would like to gratefully thank Chenyang Xu for his help in writing Section 2.1, and especially for providing us with a proof of  ... 
arXiv:1604.05041v1 fatcat:p7fl6vd4czf2jn3qituirjesaa

Page 4047 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
The lattice of M- solid varieties of a fixed type is a sublattice of the lattice of all varieties of that type.  ...  For example, if 7 is the maximum arity of the operation symbols of type t, and if V has a finite free algebra on generators, then for any monoid M of hypersubstitutions, there is a finite M-solidity testing  ... 

Homogeneous locally finite varieties

Ross Willard
1992 Algebra Universalis  
Let ~ be a locally finite variety of finite type. :U is homogeneous iff every isomorphism between subalgebras of a finite algebra in the variety extends to an automorphism of the algebra.  ...  In [5] it was shown that if ~K is homogeneous and finite axiomatizable, then it is the varietal product of some generalized G-sets and some generalized modules over a finite semisimple ring.  ...  In [5] it was shown that if ~K is homogeneous and finite axiomatizable, then it is the varietal product of some generalized G-sets and some generalized modules over a finite semisimple ring.  ... 
doi:10.1007/bf01190611 fatcat:mz35hvey5zft3fpj2p7fgyrcqm

Unpolarized Shafarevich conjectures for hyper-Kähler varieties [article]

Lie Fu, Zhiyuan Li, Teppei Takamatsu, Haitao Zou
2022 arXiv   pre-print
In a similar fashion, generalizing a result of Orr and Skorobogatov on K3 surfaces, we prove the finiteness of geometric isomorphism classes of hyper-K\"ahler varieties of CM type in a given deformation  ...  The Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collection of places.  ...  T.T. owes deep gratitude to his advisor Naoki Imai for encouragement and helpful advice and to Tetsushi Ito and Yoichi Mieda for helping him at various parts of the paper, including the proof of Theorem  ... 
arXiv:2203.10391v1 fatcat:ty6z2foggnfcldg6u6jtgf5a5y

Page 3755 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews  
Any such hypersubstitution can be inductively extended to a map on the set of all terms of the type, and hence to all identities of the type as well.  ...  A hypersubstitution of type t is a map which associates to each fundamental operation symbol of the type a term of the type, of the same arity.  ... 

From Equational Specifications of Algebras with Structure to Varieties of Data Languages (Invited Paper)

Stefan Milius, Michael Wagner
2019 Conference on Algebra and Coalgebra in Computer Science  
When instantiated for orbit-finite nominal monoids, the generic HSP theorem yields a crucial step for the proof of the first Eilenberg-type variety theorem for data languages.  ...  In addition, we use the generic HSP theorem as a key ingredient to obtain Eilenberg-type correspondences yielding algebraic characterizations of properties of regular machine behaviours.  ...  Varieties of Data Languages Since the above results also cover Reiterman-type results (via the choice of X as free algebras over finite sets) the General HSP Theorem yields a key tool for a generic algebraic  ... 
doi:10.4230/lipics.calco.2019.2 dblp:conf/calco/Milius19 fatcat:6d52hfheu5htxjevqr3dgospma

Finitely generated equational classes [article]

Erhard Aichinger, Peter Mayr
2014 arXiv   pre-print
We show that every subvariety of a finitely generated congruence permutable variety is finitely generated; in fact, we prove the more general result that if a finitely generated variety has an edge term  ...  A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra.  ...  In general, a variety V of algebras of some type F is called finitely based if there is a finite set Φ of identities such that an algebra A of type F lies in V if and only if A |= Φ.  ... 
arXiv:1403.7938v1 fatcat:j45dailtzzaqtkmzmjml2m64mm

Support varieties of ( g, k)-modules of finite type [article]

Alexey V. Petukhov
2011 arXiv   pre-print
We say that M is of finite type if M is a ( g, k)-module and Hom_ k(V, M)<∞ for any simple k-module V. Let X be a variety of all Borel subalgebras of g.  ...  Let M be a finitely generated ( g, k)-module of finite type. In this article we prove that M is holonomic, i.e. M is governed by some subvariety L_M⊂ X and some local system S_M on it.  ...  Let M be a finitely generated (g, k)-module of finite type which affords a central character and (L, S) be the corresponding pair consisting of a variety and a coherent sheaf as before.  ... 
arXiv:1101.0472v1 fatcat:trd7kjz3wndh3fnx4nbwscquqq
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