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The set of types of a finitely generated variety

1993
*
Discrete Mathematics
*

Priihle and

doi:10.1016/0012-365x(93)90219-j
fatcat:5s67pgrodrevhmrcxhfwoflr6y
*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. ...##
###
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]

2021
*
arXiv
*
pre-print

Motivated by

arXiv:2112.11408v1
fatcat:hsjcfifienartmjbj4r5rheygu
*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. ...##
###
An Introduction to Tame Congruence Theory
[chapter]

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*. ...

##
###
A field guide to equational logic

1992
*
Journal of symbolic computation
*

By way

doi:10.1016/0747-7171(92)90013-t
fatcat:ou4teabieffhhlciea4odb546i
*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 . ...##
###
On locally finite varieties with undecidable equational theory

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. ...

##
###
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]

2016
*
arXiv
*
pre-print

Our proof uses

arXiv:1604.05041v1
fatcat:p7fl6vd4czf2jn3qituirjesaa
*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*...##
###
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

1992
*
Algebra Universalis
*

Let ~ be

doi:10.1007/bf01190611
fatcat:mz35hvey5zft3fpj2p7fgyrcqm
*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. ...##
###
Unpolarized Shafarevich conjectures for hyper-Kähler varieties
[article]

2022
*
arXiv
*
pre-print

In

arXiv:2203.10391v1
fatcat:ty6z2foggnfcldg6u6jtgf5a5y
*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 ...##
###
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)

2019
*
Conference on Algebra and Coalgebra in Computer Science
*

When instantiated for orbit-

doi:10.4230/lipics.calco.2019.2
dblp:conf/calco/Milius19
fatcat:6d52hfheu5htxjevqr3dgospma
*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 ...##
###
Finitely generated equational classes
[article]

2014
*
arXiv
*
pre-print

We show that every subvariety

arXiv:1403.7938v1
fatcat:j45dailtzzaqtkmzmjml2m64mm
*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. ...##
###
Support varieties of ( g, k)-modules of finite type
[article]

2011
*
arXiv
*
pre-print

We say that M is

arXiv:1101.0472v1
fatcat:trd7kjz3wndh3fnx4nbwscquqq
*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. ...
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