Finite orthodox locally idempotent semigroups having no finite basis of biidentities

Let W be a finite language and let Wc be the closure of W under taking subwords. Let S(W) denote the Rees quotient of a free monoid over the ideal consisting of all words that are not in Wc. We call W finitely based if the monoid S(W) is finitely based. Although these semigroups have easy structure they behave "generically" with respect to the finite basis property [6]. In this paper, we describe all finitely based words in a two-letter alphabet. We also find some necessary and some sufficient conditions for a set of words to be finitely based.

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On Finite Basis Property for Joins of Varieties of Associative Rings

Communications in Algebra ◽

10.1080/00927870903200836 ◽

2010 ◽

Vol 38 (9) ◽

pp. 3187-3205

Author(s):

Nikolay Silkin

Keyword(s):

Basis Property ◽

Finite Basis ◽

Finite Basis Property ◽

Joins Of Varieties ◽

Associative Rings

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A nonassociative algebra having no finite basis for its laws

Siberian Mathematical Journal ◽

10.1007/bf00969242 ◽

1978 ◽

Vol 18 (6) ◽

pp. 1007-1008 ◽

Cited By ~ 3

Author(s):

Yu. N. Mal'tsev ◽

V. A. Parfenov

Keyword(s):

Finite Basis ◽

Nonassociative Algebra

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Application of B-splines finite basis sets to relativistic two-photon decay rates of $\mathsf{2s}$ level in hydrogenic ions

The European Physical Journal D ◽

10.1007/s100530050147 ◽

1998 ◽

Vol 3 (1) ◽

pp. 43-52 ◽

Cited By ~ 40

Author(s):

J.P. Santos ◽

F. Parente ◽

P. Indelicato

Keyword(s):

Finite Basis ◽

Decay Rates ◽

Basis Sets ◽

B Splines ◽

Two Photon ◽

Photon Decay ◽

Hydrogenic Ions

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Nonreactive atom/molecule-surface scattering within the finite basis wave packet method

Computer Physics Communications ◽

10.1016/0010-4655(96)00064-1 ◽

1996 ◽

Vol 97 (3) ◽

pp. 331-344 ◽

Cited By ~ 13

Author(s):

Didier Lemoine

Keyword(s):

Wave Packet ◽

Finite Basis ◽

Surface Scattering ◽

Molecule Surface

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Comparison of the polarizabilities and hyperpolarizabilities obtained from finite basis set and finite difference Hartree-Fock calculations for diatomic molecules

Journal of Physics B Atomic Molecular and Optical Physics ◽

10.1088/0953-4075/34/24/314 ◽

2001 ◽

Vol 34 (24) ◽

pp. 5127-5143 ◽

Cited By ~ 23

Author(s):

J Kobus ◽

D Moncrieff ◽

S Wilson

Keyword(s):

Finite Difference ◽

Diatomic Molecules ◽

Finite Basis ◽

Basis Set ◽

Hartree Fock

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On the finite basis problem for certain 2-limited words

Acta Mathematica Sinica English Series ◽

10.1007/s10114-012-0193-1 ◽

2012 ◽

Vol 29 (3) ◽

pp. 571-590 ◽

Cited By ~ 6

Author(s):

Jian Rong Li ◽

Wen Ting Zhang ◽

Yan Feng Luo

Keyword(s):

Finite Basis ◽

Finite Basis Problem ◽

Basis Problem

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A general finite basis condition for systems of semigroup identities

Semigroup Forum ◽

10.1007/bf02573389 ◽

1990 ◽

Vol 41 (1) ◽

pp. 181-191 ◽

Cited By ~ 1

Author(s):

M. V. Volkov

Keyword(s):

Finite Basis ◽

Semigroup Identities

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Categorical Functional Data Analysis. The cfda R Package

Mathematics ◽

10.3390/math9233074 ◽

2021 ◽

Vol 9 (23) ◽

pp. 3074

Author(s):

Cristian Preda ◽

Quentin Grimonprez ◽

Vincent Vandewalle

Keyword(s):

Functional Data ◽

Multiple Correspondence Analysis ◽

Real Data ◽

Jump Process ◽

R Package ◽

Finite Basis ◽

Data Set ◽

Stochastic Jump ◽

Finite Set ◽

Infinite Set

Categorical functional data represented by paths of a stochastic jump process with continuous time and a finite set of states are considered. As an extension of the multiple correspondence analysis to an infinite set of variables, optimal encodings of states over time are approximated using an arbitrary finite basis of functions. This allows dimension reduction, optimal representation, and visualisation of data in lower dimensional spaces. The methodology is implemented in the cfda R package and is illustrated using a real data set in the clustering framework.

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