A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Reducibility of pointlike problems

2015
*
Semigroup Forum
*

We show that the

doi:10.1007/s00233-015-9769-2
fatcat:tzeixxtrinbube46k2nca2qrte
*pointlike*and the*idempotent**pointlike*problems are reducible with respect to natural signatures in the following cases: the pseudovariety of all finite semigroups in which the order of ... Allowing only trivial groups, we obtain omega-reducibility of the*pointlike*and*idempotent**pointlike*problems, respectively for the pseudovarieties of all finite aperiodic semigroups (A) and of all finite ... Hence V is σ-reducible for*idempotent**pointlike**sets*. Corollary 4.4. ...##
###
Pointlike sets with respect to R and J

2008
*
Journal of Pure and Applied Algebra
*

We also give an algorithm to compute J-

doi:10.1016/j.jpaa.2007.06.007
fatcat:3hpz5siwhfduhc4hnxg7o46zky
*pointlike**sets*, where J denotes the pseudovariety of all finite J-trivial semigroups. ... We finally show that, in contrast with the situation for R, the natural adaptation of Henckell's algorithm to J computes*pointlike**sets*, but not all of them. ... Henckell presented algorithms for computing A-*pointlike**sets*[17] and A-*idempotent**pointlike**sets*[18] for the pseudovariety A of aperiodic semigroups. ...##
###
COMPLEXITY PSEUDOVARIETIES ARE NOT LOCAL: TYPE II SUBSEMIGROUPS CAN FALL ARBITRARILY IN COMPLEXITY

2006
*
International journal of algebra and computation
*

Since H is V-

doi:10.1142/s0218196706003177
fatcat:wco6wgce4zeevhdtbfbzr7tao4
*idempotent**pointlike*, there is an*idempotent*e of T with H ≤ e ϕ −1 2 . Let q ∈ xϕ. Then xH ⊆ q ϕ −1 1 H ⊆ (q e )ϕ −1 1 .*Setting*q = q e completes the proof. ... Since H is a group and is V-*pointlike*, our above observations show that H is in fact V-*idempotent**pointlike*.*Set*x = (a 0 , 1, 0 ), y = (a 0 , 1, 2 ). Notice that xH = yH = {x, y}. ...##
###
Page 8909 of Mathematical Reviews Vol. , Issue 2002M
[page]

2002
*
Mathematical Reviews
*

In the 1970s, Henckell and Rhodes introduced the notion of a

*pointlike**set*: For a pseudovariety V of monoids, a subset Y of a finite monoid S is said to be V-*pointlike*if for every relational morphism ... In order to prove his result, the author first generalizes the notion of*pointlike**sets*to categories, studying how*pointlikes*for V and gV (the pseudovariety of categories generated by monoids in V viewed ...##
###
A Profinite Approach to Stable Pairs
[article]

2006
*
arXiv
*
pre-print

We give a short proof, using profinite techniques, that

arXiv:math/0612497v1
fatcat:trkdsu7psvfybmot53sd2ljxk4
*idempotent**pointlikes*, stable pairs and triples are decidable for the pseudovariety of aperiodic monoids. ... Then the maximal V-*idempotent**pointlikes*of M are precisely the maximal*idempotents*of PL V (M ).Proof. We already observed that*idempotents*of PL V (M ) are V-*idempotent**pointlike*. ... Also the*set*of V-*idempotent**pointlikes*of M form a downwards closed subset of P (M ). Next we consider the notion of a V-stable pair. ...##
###
Page 3002 of Mathematical Reviews Vol. , Issue 2001E
[page]

2001
*
Mathematical Reviews
*

The author considers the operation S ++ Ag(S), where Ag(S) is the

*set*of all G-*pointlike*subsets of S, a semigroup under sub-*set*multiplication; and the associated operation on pseudovarieties of finite ... A subset ¥ of a finite semigroup S is group-*pointlike*, or G-*pointlike*, if for each relational morphism t: S — G into a finite group G, X¥ C r~'(g) for some g € G. ...##
###
An application of a Theorem of Ash to finite covers

2004
*
Studia Logica: An International Journal for Symbolic Logic
*

We show how the existence of nite proper covers for semigroups in this quasivariety is a consequence of Ash's celebrated theorem for

doi:10.1007/s11225-005-5057-6
fatcat:3wypmtuieravnb5nvkfpmoghnq
*pointlike**sets*. Date: November 7, 2001. ... satis ed for all elements a and*idempotents*e. ... We begin with the well known characterisation of*pointlike**sets*(see Theorem 1.2 of 8]) which is a consequence of Ash's theorem (Theorem 2.1 in 1]) and the fact that in a semigroup in which the*idempotents*...##
###
Pointlike sets with respect to ER
[article]

2022
*
arXiv
*
pre-print

We show that

arXiv:2204.09247v1
fatcat:kvcqh7xk2jeqze45r6cpywzbf4
*pointlike**sets*are decidable for the pseudovariety of finite semigroups whose*idempotent*-generated subsemigroup is R-trivial. ... Notably, our proof is constructive: we provide an explicit relational morphism which computes the ER-*pointlike*subsets of a given finite semigroup. ... General theory of*pointlike**sets*4.1. In this section we will briefly cover key aspects of the authors' "general theory of*pointlike**sets*" which provides the framework for our work here. ...##
###
Some reducibility properties for pseudovarieties of the form DRH
[article]

2015
*
arXiv
*
pre-print

The classes of systems considered (of

arXiv:1512.01021v1
fatcat:4oflivhxenddxclaoozs4qk7si
*pointlike*,*idempotent**pointlike*and graph equations) are known to play a role in decidability questions concerning pseudovarieties of the forms V * W, V join W, and ...*idempotent**pointlike*equations (x 1 = · · · = x n = x 2 n ). ... The subsequent sections focus on*pointlike*, graph, and*idempotent**pointlike*equations, in this order. ...##
###
Some reducibility properties for pseudovarieties of the form DRH

2017
*
Communications in Algebra
*

The classes of systems considered (of

doi:10.1080/00927872.2017.1360328
fatcat:s5sjq5mp6jcktc7pmgzhczth6e
*pointlike*,*idempotent**pointlike*and graph equations) are known to play a role in decidability questions concerning pseudovarieties of the forms V * W, V ∨ W, and V ...*Idempotent**pointlike*equations We now take for C the class of all systems of*idempotent**pointlike*equations. ...*idempotent**pointlike*equations (x 1 = · · · = x n = x 2 n ). ...##
###
Page 4352 of Mathematical Reviews Vol. , Issue 2000f
[page]

2000
*
Mathematical Reviews
*

In particular, it is proved that the join of a pseudovariety, for which

*pointlike**sets*are com- putable, with a pseudovariety, whose free objects are finite and computable, has again computable*pointlike*...*sets*. ...##
###
Pointlike reducibility of pseudovarieties of the form V ∗D

2016
*
International journal of algebra and computation
*

We establish a connection between

doi:10.1142/s0218196716500090
fatcat:tv3mpnkeevg4pgdevcrqeukct4
*pointlike*reducibility of V* D and the*pointlike*reducibility of the pseudovariety V. ... In particular, for the canonical signature κ consisting of the multiplication and the (ω-1)-power, we show that V* D is*pointlike*κ-reducible when V is*pointlike*κ-reducible. ... One says that V has decidable*pointlikes*if one can effectively compute all the V-*pointlike**sets*of any given finite semigroup. ...##
###
A General Theory of Pointlike Sets
[article]

2021
*
arXiv
*
pre-print

We introduce a general unifying framework for the investigation of

arXiv:2108.12824v1
fatcat:tufwsqdlnbfshc7naxyovio3yy
*pointlike**sets*. ... Notably, this provides a characterization of*pointlikes*which does not mention relational morphisms. Along the way, we formalize various common heuristics and themes in the study of*pointlike**sets*. ...*pointlike*context EP W = 1 − Like W , which assigns S ∈ FinSgp to its*set*of W-*idempotent**pointlike*subsemigroups, which are subsemigroups T of S such that whenever ρ : S W is a relational morphism with ...##
###
Profinite Semigroups, Mal'cev Products, and Identities

1996
*
Journal of Algebra
*

We also characterize the

doi:10.1006/jabr.1996.0192
fatcat:x7oglqvmvve73jnbma5ow24qoq
*pointlike*subsets of a finite semigroup by means of a relational morphism into a profinite semigroup. ... Abstract: We compute a*set*of identities defining the Mal'cev product of pseudovarieties of finite semigroups or finite ordered semigroups. ... Moreover, we verify that a subset X of a finite semigroup S is a V-*pointlike*if and only if it is a V -*pointlike*. Suppose indeed that X is a V -*pointlike*subset. ...##
###
The G-Exponent of a Pseudovariety of Semigroups

2000
*
Journal of Algebra
*

Ash's proof of the

doi:10.1006/jabr.1999.7993
fatcat:c4llyd2xsrcynbzbk4mnto3wsy
*Pointlike*Conjecture provides an algorithm for calculating the group-*pointlike*subsets of a finite semigroup S. ... We show that 3 G V = S for any pseudovariety of semigroups V that contains a semigroup such that the subsemigroup generated by its*idempotents*is non-permutative. ... If S is a semigroup then E S denotes the*set*of*idempotents*of S and, for x ∈ S, x −1 and x 1 denote, respectively, the*sets*s ∈ S sxs = s and x . ...
« Previous

*Showing results 1 — 15 out of 167 results*