## Finite integral relation algebras (1985)

Venue: | Universal Algebra and Lattice Theory, Lecture Notes in Mathematics 1149 |

Citations: | 3 - 0 self |

### BibTeX

@INPROCEEDINGS{Maddux85finiteintegral,

author = {Roger D. Maddux},

title = {Finite integral relation algebras},

booktitle = {Universal Algebra and Lattice Theory, Lecture Notes in Mathematics 1149},

year = {1985},

pages = {175--197},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

Please note that this paper does not exist. It consists entirely of excerpts from the

### Citations

187 |
Boolean algebras with operators
- Jónsson, Tarski
- 1951
(Show Context)
Citation Context ...nite. Then A is a perfect extension of itself and A ∼ = A + . Let 3 ≤ n < ω. Let BnA be the set of those n-by-n matrices of atoms of A which satisfy the following conditions for all i, j, k < n: (14) =-=(15)-=- (16) aii ≤ 1 , , ăij = aji, aik ≤ aij ;ajk. It is known that A ∈ RAn iff A has an n-dimensional relational basis. Since BnA is a finite set and an n-dimensional relational basis for A is a special so... |

65 |
The representation of relational algebras
- Lyndon
- 1950
(Show Context)
Citation Context ... Then A is a perfect extension of itself and A ∼ = A + . Let 3 ≤ n < ω. Let BnA be the set of those n-by-n matrices of atoms of A which satisfy the following conditions for all i, j, k < n: (14) (15) =-=(16)-=- aii ≤ 1 , , ăij = aji, aik ≤ aij ;ajk. It is known that A ∈ RAn iff A has an n-dimensional relational basis. Since BnA is a finite set and an n-dimensional relational basis for A is a special sort of... |

57 | Tarski: Distributive and modular laws in the arithmetic of relation algebras - Chin, A - 1951 |

45 | On representable relation algebras - Monk - 1964 |

18 | Representations of integral relation algebras - McKenzie - 1970 |

15 | Representability is not decidable for finite relation algebras
- Hirsch, Hodkinson
(Show Context)
Citation Context ...abd] [acd] [bcd] Table 3. Cycles needed for 4527 algebras, by atomss6 ROGER D. MADDUX algorithm for determing whether a finite RA is in RRA, and indeed there is not, as was proved by Hirsch-Hodkinson =-=[14]-=-. On the other hand, if A ∈ RA ∼ RRA, then this fact can be detected, either by eventually finding that A has no relational basis of a some finite dimension, or else by checking each of the equations ... |

15 | Representation of modular lattices and of relation algebras - Jónsson - 1959 |

14 |
The representation of relation algebras
- McKenzie
- 1966
(Show Context)
Citation Context ...N ALGEBRAS 3 Over the years several mathematicians have attempted to enumerate small finite relation algebras in which 1 , is an atom. This includes R. Lyndon [16, fn. 13], F. Backer [2], R. McKenzie =-=[19]-=-, U. Wostner [21], B. McEvoy, S. Comer [3, 13], P. Jipsen, E. Lukács, R. Kramer, myself, and quite probably several others. The numbers are shown in Table 1. Lyndon found the numbers of relation algeb... |

10 | Algebras with Operators - Boolean - 1952 |

10 | varieties containing relation algebras - Some - 1982 |

6 | Representations for small relation algebras
- Andr'eka, Maddux
- 1994
(Show Context)
Citation Context ...the spectrum of a nontrivial direct product of finite relation algebras is also ∅. The spectra of the algebras 11, 12, 22, 13, 23, 33, 17, 27, 37, 47, 57, 67, and 77 were determined in Andréka-Maddux =-=[1]-=-. We say ρ is a square representation of A ∈ RA on U ∈ V if ρ is an embedding of A into Re (U). We say that a square representation ρ of A on U is unique if there is no other square representation of ... |

4 |
Finite integral relation algebras, Universal Algebra and Lattice Theory, Springer-Verlag
- Maddux
- 1985
(Show Context)
Citation Context ... 1)! (n − s) 2 � !2 1 2 (n−s) whenever s ≤ n ∈ ω and n − s is even. Let F (n, s) be the number of isomorphism types of integral relation algebras with n atoms and s symmetric atoms. Theorem 1 (Maddux =-=[18]-=-). An asymptotic formula for the number of finite integral relation algebras with n atoms and s symmetric atoms: F (n, s) ∼ 2Q(n,s) P (n, s) = 2 1 6 (n−1)((n−1)2 +3s−1) (s − 1)! � 1 2 (n − s)� !2 1 2 ... |

4 | Contributions to the theory of models. III, Koninklijke Nederlandse Akademie van Wetenschappen - Tarski |

3 | Embedding modular lattices into relation algebras - Maddux - 1981 |

2 | of integral relation algebras - Representations - 1970 |

2 |
Finite relation algebras,” Notices of the American
- Wostner
- 1976
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Citation Context ... the years several mathematicians have attempted to enumerate small finite relation algebras in which 1 , is an atom. This includes R. Lyndon [16, fn. 13], F. Backer [2], R. McKenzie [19], U. Wostner =-=[21]-=-, B. McEvoy, S. Comer [3, 13], P. Jipsen, E. Lukács, R. Kramer, myself, and quite probably several others. The numbers are shown in Table 1. Lyndon found the numbers of relation algebras with at most ... |

1 |
Representable relation algebras, Report for a seminar on relation algebras conducted by A
- Backer
- 1970
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Citation Context ... INTEGRAL RELATION ALGEBRAS 3 Over the years several mathematicians have attempted to enumerate small finite relation algebras in which 1 , is an atom. This includes R. Lyndon [16, fn. 13], F. Backer =-=[2]-=-, R. McKenzie [19], U. Wostner [21], B. McEvoy, S. Comer [3, 13], P. Jipsen, E. Lukács, R. Kramer, myself, and quite probably several others. The numbers are shown in Table 1. Lyndon found the numbers... |

1 |
Multivalued loops and their connection with algebraic logic
- Comer
- 1979
(Show Context)
Citation Context ...ticians have attempted to enumerate small finite relation algebras in which 1 , is an atom. This includes R. Lyndon [16, fn. 13], F. Backer [2], R. McKenzie [19], U. Wostner [21], B. McEvoy, S. Comer =-=[3, 13]-=-, P. Jipsen, E. Lukács, R. Kramer, myself, and quite probably several others. The numbers are shown in Table 1. Lyndon found the numbers of relation algebras with at most three atoms. Comer first comp... |

1 |
schemes forbidding monochrome triangles
- Color
- 1983
(Show Context)
Citation Context ...hese 37 algebras, 27 are in RA5 and the other 10 are not in RA5 (and not representable). S. D. Comer has accumulated representations for many finite relation algebras with up to four atoms; see Comer =-=[6, 4, 5, 7, 8, 9, 10, 11, 12]-=-. Comer found representations for all but five of the 102 algebras 137, . . . , 3737, 165, . . . , 6565. One of these five algebras was 2837, in which (J), (L), and (M) hold and yet there is no 5-dime... |

1 |
of color schemes, Acta
- Constructions
- 1983
(Show Context)
Citation Context ...hese 37 algebras, 27 are in RA5 and the other 10 are not in RA5 (and not representable). S. D. Comer has accumulated representations for many finite relation algebras with up to four atoms; see Comer =-=[6, 4, 5, 7, 8, 9, 10, 11, 12]-=-. Comer found representations for all but five of the 102 algebras 137, . . . , 3737, 165, . . . , 6565. One of these five algebras was 2837, in which (J), (L), and (M) hold and yet there is no 5-dime... |

1 |
derived from cogroups
- Polygroups
- 1984
(Show Context)
Citation Context ...hese 37 algebras, 27 are in RA5 and the other 10 are not in RA5 (and not representable). S. D. Comer has accumulated representations for many finite relation algebras with up to four atoms; see Comer =-=[6, 4, 5, 7, 8, 9, 10, 11, 12]-=-. Comer found representations for all but five of the 102 algebras 137, . . . , 3737, 165, . . . , 6565. One of these five algebras was 2837, in which (J), (L), and (M) hold and yet there is no 5-dime... |

1 |
regular trees and their color algebras
- Weakly
- 1988
(Show Context)
Citation Context |

1 |
Algebras and their Graphical Representation
- Multi-Valued
- 1986
(Show Context)
Citation Context ...ticians have attempted to enumerate small finite relation algebras in which 1 , is an atom. This includes R. Lyndon [16, fn. 13], F. Backer [2], R. McKenzie [19], U. Wostner [21], B. McEvoy, S. Comer =-=[3, 13]-=-, P. Jipsen, E. Lukács, R. Kramer, myself, and quite probably several others. The numbers are shown in Table 1. Lyndon found the numbers of relation algebras with at most three atoms. Comer first comp... |