Products of idempotent endomorphisms of an independence algebra of infinite rank

DOI10.1017/S0305004100071607zbMath0819.20070MaRDI QIDQ4277218

Andrew Lewin, J. B. Fountain

Publication date: 24 February 1994

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

universal algebraminimal generating setsexchange propertysingular endomorphismsidempotent generated semigroupssingular idempotent endomorphismsstrong independence algebras

Mathematics Subject Classification ID

Semigroups of transformations, relations, partitions, etc. (20M20) Free semigroups, generators and relations, word problems (20M05) Free algebras (08B20) Relational systems, laws of composition (08A02) Automorphisms and endomorphisms of algebraic structures (08A35)

Related Items (32)

Matrix theory for independence algebras ⋮ Factorisable Semigroups of Linear Transformations ⋮ Relative ranks in the monoid of endomorphisms of an independence algebra. ⋮ Products of idempotent endomorphisms of free acts of infinite rank ⋮ Variants of finite full transformation semigroups ⋮ Motzkin monoids and partial Brauer monoids ⋮ Diagram monoids and Graham-Houghton graphs: idempotents and generating sets of ideals ⋮ The depth of the semigroup of balanced endomorphisms ⋮ Primitive groups synchronize non-uniform maps of extreme ranks ⋮ Unit-regular and semi-balanced elements in various semigroups of transformations ⋮ Idempotents and one-sided units: lattice invariants and a semigroup of functors on the category of monoids ⋮ Primitive groups, graph endomorphisms and synchronization ⋮ Regularity and products of idempotents in endomorphism monoids of projective acts ⋮ Product decompositions of semigroups induced by action pairs ⋮ Defining relations for idempotent generators in finite full transformation semigroups. ⋮ Independence algebras, basis algebras and the distributivity condition ⋮ A DESCRIPTION OF NORMAL SEMIGROUPS OF ENDOMORPHISMS OF PROPER INDEPENDENCE ALGEBRAS ⋮ The largest subsemilattices of the endomorphism monoid of an independence algebra. ⋮ Conjugation in semigroups. ⋮ Regular centralizers of idempotent transformations. ⋮ Products of two idempotent transformations over arbitrary sets and vector spaces ⋮ A characterization of selfmaps which are composites of three projections ⋮ Independence algebras, basis algebras and semigroups of quotients ⋮ Congruences on the partial automorphism monoid of a free group action ⋮ Idempotent endomorphisms of an independence algebra of finite rank ⋮ Automorphisms of Endomorphism Monoids of 1-Simple Free Algebras ⋮ Decomposition of singular elements of an algebra into product of idempotents, a survey ⋮ Idempotent Generation in the Endomorphism Monoid of a Uniform Partition ⋮ Idempotents and one-sided units in infinite partial Brauer monoids ⋮ Presentations for singular wreath products ⋮ v*-ALGEBRAS, INDEPENDENCE ALGEBRAS AND LOGIC ⋮ Generators and factorisations of transformation semigroups

Cites Work

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• Free idempotent generated semigroups and endomorphism monoids of independence algebras
• On regular semigroups
• Products of idempotent linear transformations
• Some subsemigroups of infinite full transformation semigroups
• The Subsemigroup Generated By the Idempotents of a Full Transformation Semigroup

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