Abstract
A constellation is a set with a partially-defined binary operation
and a unary operation satisfying certain conditions, which, loosely speaking,
provides a ‘one-sided’ analogue of a category, where we have a notion of ‘domain’
but not of ‘range’. Upon the introduction of an ordering, we may define
so-called inductive constellations. These prove to be a significant tool in the
study of an important class of semigroups, termed left restriction semigroups,
which arise from the study of systems of partial transformations. In this paper,
we study the defining conditions for (inductive) constellations and determine
that certain of the original conditions from previous papers are redundant.
Having weeded out this redundancy, we show, by the construction of suitable
counterexamples, that the remaining conditions are independent.
References
- M. Beeson, Lambda logic, in Automated reasoning, Lecture Notes in Computer Sciences 3097, Springer, Berlin, pp. 460–474.
- A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Volume , Mathematical Surveys of the Amer. Math. Soc., No. 7, Amer. Math. Soc., Providence, R. I., 1961.
- J. Fountain, A class of right PP monoids, Quart. J. Math. Oxford, (2), 28 (1977), 285–300.
- J. Fountain, Adequate semigroups, Proc. Edinb. Math. Soc., (2), 22 (1979), –125.
- V. Gould and C. Hollings, Partial actions of inverse and weakly left E-ample semigroups J. Austral. Math. Soc. 86(3) (2009), 355–377.
- V. Gould and C. Hollings, Restriction semigroups and inductive constellations, Comm. Algebra, 38(1) (2010), 261–287.
- V. Gould and C. Hollings, Actions and partial actions of inductive constella- tions, Semigroup Forum, 82(1) (2011), 35–60.
- C. Hollings, Partial Actions of Semigroups and Monoids, PhD thesis, Univer- sity of York, 2007.
- C. Hollings, From right PP monoids to restriction semigroups: a survey, Eu- rop. J. Pure Appl. Math. 2(1) (2009), 21–57.
- C. Hollings, Extending the Ehresmann-Schein-Nambooripad Theorem, Semi- group Forum, 80(3) (2010), 453–476.
- M. Jackson and T. Stokes, Agreeable semigroups, J. Algebra, 226 (2003), 393–
- M. V. Lawson, Inverse Semigroups: The Theory of Partial Symmetries, World ScientiŞc, 1998.
- Prover9 and Mace4, http://www.cs.unm.edu/∼mccune/prover9/ Christopher Hollings Mathematical Institute –29 St. Giles’ Oxford, OX1 3LB United Kingdom e-mail: christopher.hollings@maths.ox.ac.uk
Abstract
References
- M. Beeson, Lambda logic, in Automated reasoning, Lecture Notes in Computer Sciences 3097, Springer, Berlin, pp. 460–474.
- A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Volume , Mathematical Surveys of the Amer. Math. Soc., No. 7, Amer. Math. Soc., Providence, R. I., 1961.
- J. Fountain, A class of right PP monoids, Quart. J. Math. Oxford, (2), 28 (1977), 285–300.
- J. Fountain, Adequate semigroups, Proc. Edinb. Math. Soc., (2), 22 (1979), –125.
- V. Gould and C. Hollings, Partial actions of inverse and weakly left E-ample semigroups J. Austral. Math. Soc. 86(3) (2009), 355–377.
- V. Gould and C. Hollings, Restriction semigroups and inductive constellations, Comm. Algebra, 38(1) (2010), 261–287.
- V. Gould and C. Hollings, Actions and partial actions of inductive constella- tions, Semigroup Forum, 82(1) (2011), 35–60.
- C. Hollings, Partial Actions of Semigroups and Monoids, PhD thesis, Univer- sity of York, 2007.
- C. Hollings, From right PP monoids to restriction semigroups: a survey, Eu- rop. J. Pure Appl. Math. 2(1) (2009), 21–57.
- C. Hollings, Extending the Ehresmann-Schein-Nambooripad Theorem, Semi- group Forum, 80(3) (2010), 453–476.
- M. Jackson and T. Stokes, Agreeable semigroups, J. Algebra, 226 (2003), 393–
- M. V. Lawson, Inverse Semigroups: The Theory of Partial Symmetries, World ScientiŞc, 1998.
- Prover9 and Mace4, http://www.cs.unm.edu/∼mccune/prover9/ Christopher Hollings Mathematical Institute –29 St. Giles’ Oxford, OX1 3LB United Kingdom e-mail: christopher.hollings@maths.ox.ac.uk
Details
| Other ID | JA46PV99ZB |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | December 1, 2011 |
| Published in Issue | Year 2011 Volume: 10 Issue: 10 |