Finite involution semigroups with infinite irredundant bases of identities
-
Edmond W. H. Lee
Abstract
A basis of identities for an algebra is irredundant if each of its proper subsets fails to be a basis for the algebra. The first known examples of finite involution semigroups with infinite irredundant bases are exhibited. These involution semigroups satisfy several counterintuitive properties: their semigroup reducts do not have irredundant bases, they share reducts with some other finitely based involution semigroups, and they are direct products of finitely based involution semigroups.
Correction Statement
Correction added after online publication 11 September 2015:
For the readers convenience equation (7.2a) has been changed from
The author would like to thank the anonymous referees for helpful suggestions, and Igor Dolinka and Marcel G. Jackson for very fruitful discussions.
© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- The elliptic trilogarithm and Mahler measures of K3 surfaces
- Morphisms determined by objects and flat covers
- Graev ultrametrics and free products of Polish groups
- Critical values of Rankin–Selberg L-functions for GLn × GLn-1 and the symmetric cube L-functions for GL2
- Simple connectivity in polar spaces
- On the μ-invariant of Katz p-adic L-functions attached to imaginary quadratic fields
- Non-existence of certain Einstein metrics on some symplectic manifolds
- A note on real algebraic groups
- Coercive and noncoercive nonlinear Neumann problems with indefinite potential
- No universal group in a cardinal
- Finite involution semigroups with infinite irredundant bases of identities
Artikel in diesem Heft
- Frontmatter
- The elliptic trilogarithm and Mahler measures of K3 surfaces
- Morphisms determined by objects and flat covers
- Graev ultrametrics and free products of Polish groups
- Critical values of Rankin–Selberg L-functions for GLn × GLn-1 and the symmetric cube L-functions for GL2
- Simple connectivity in polar spaces
- On the μ-invariant of Katz p-adic L-functions attached to imaginary quadratic fields
- Non-existence of certain Einstein metrics on some symplectic manifolds
- A note on real algebraic groups
- Coercive and noncoercive nonlinear Neumann problems with indefinite potential
- No universal group in a cardinal
- Finite involution semigroups with infinite irredundant bases of identities
