Relative ranks in the monoid of endomorphisms of an independence algebra

被引：17

作者：

Araujo, J. ^{[1
]}

Mitchell, J. D.

机构：

[1] Univ Aberta, R Escola Politecn 147, P-1269001 Lisbon, Portugal

[2] Univ Lisbon, Ctr Algebra, P-1699 Lisbon, Portugal

[3] Univ St Andrews, Inst Math, St Andrews KY16 9SS, Fife, Scotland

来源：

MONATSHEFTE FUR MATHEMATIK | 2007年 / 151卷 / 01期

关键词：

independence algebras; endomorphisms; relative rank; TRANSFORMATION SEMIGROUPS; IDEMPOTENT ENDOMORPHISMS; GENERATORS; PRODUCTS; SETS;

D O I：

10.1007/s00605-006-0433-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The relative ranks of the monoid of endomorphisms of a strong independence algebra of infinite rank modulo two distinguished subsets are calculated. These subsets are the group of automorphisms and the endomorphisms alpha satisfying alpha(2) = alpha. The extra generators are characterised in each case.

引用

页码：1 / 10

页数：10

共 14 条

[1] On generating countable sets of endomorphisms [J].

Araújo, J ;

Mitchell, JD ;

Silva, N .

ALGEBRA UNIVERSALIS, 2003, 50 (01) :61-67

[2] Normal semigroups of endomorphisms of proper independence algebras are idempotent generated [J].

Araújo, J .

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2002, 45 :205-217

[3]

Araújo J, 2002, ALGEBR COLLOQ, V9, P375

[4] Independence algebras [J].

Cameron, PJ ;

Szabó, C .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2000, 61 :321-334

[5]

CICHON J, 2007, IN PRESS T AM MATH S

[6] PRODUCTS OF IDEMPOTENT ENDOMORPHISMS OF AN INDEPENDENCE ALGEBRA OF INFINITE RANK [J].

FOUNTAIN, J ;

LEWIN, A .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1993, 114 :303-319

[7] PRODUCTS OF IDEMPOTENT ENDOMORPHISMS OF AN INDEPENDENCE ALGEBRA OF FINITE RANK [J].

FOUNTAIN, J ;

LEWIN, A .

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1992, 35 :493-500

[8] INDEPENDENCE ALGEBRAS [J].

GOULD, V .

ALGEBRA UNIVERSALIS, 1995, 33 (03) :294-318

[9] Countable versus uncountable ranks in infinite semigroups of transformations and relations [J].

Higgins, PM ;

Howie, JM ;

Mitchell, JD ;

Ruskuc, N .

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2003, 46 :531-544

[10] Generators and factorisations of transformation semigroups [J].

Higgins, PM ;

Howie, JM ;

Ruskuc, N .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1998, 128 :1355-1369

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