### Abstract

We consider noncomplete continuous and algebraic lattices and prove that finitely generated free lattices are algebraic. We also study the Lawson topology, the second most important topology in the theory of continuous domains, on finitely presented lattices. In particular, we prove that algebraic finitely presented lattices are linked bicontinuous and the Lawson topology on these lattices coincides with the interval topology. Several examples of non-distributive and noncomplete algebraic and continuous lattices are given in the paper.

Original language | English |
---|---|

Pages (from-to) | 215-230 |

Number of pages | 16 |

Journal | Algebra Universalis |

Volume | 46 |

Issue number | 1-2 |

Publication status | Published - 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Continuous
- Finitely presented
- Interval topology
- Lattice
- Lawson topology

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Algebra Universalis*,

*46*(1-2), 215-230.

**On continuous noncomplete lattices.** / Adaricheva, K. V.; Gorbunov, V. A.; Semenova, M. V.

Research output: Contribution to journal › Article

*Algebra Universalis*, vol. 46, no. 1-2, pp. 215-230.

}

TY - JOUR

T1 - On continuous noncomplete lattices

AU - Adaricheva, K. V.

AU - Gorbunov, V. A.

AU - Semenova, M. V.

PY - 2001

Y1 - 2001

N2 - We consider noncomplete continuous and algebraic lattices and prove that finitely generated free lattices are algebraic. We also study the Lawson topology, the second most important topology in the theory of continuous domains, on finitely presented lattices. In particular, we prove that algebraic finitely presented lattices are linked bicontinuous and the Lawson topology on these lattices coincides with the interval topology. Several examples of non-distributive and noncomplete algebraic and continuous lattices are given in the paper.

AB - We consider noncomplete continuous and algebraic lattices and prove that finitely generated free lattices are algebraic. We also study the Lawson topology, the second most important topology in the theory of continuous domains, on finitely presented lattices. In particular, we prove that algebraic finitely presented lattices are linked bicontinuous and the Lawson topology on these lattices coincides with the interval topology. Several examples of non-distributive and noncomplete algebraic and continuous lattices are given in the paper.

KW - Continuous

KW - Finitely presented

KW - Interval topology

KW - Lattice

KW - Lawson topology

UR - http://www.scopus.com/inward/record.url?scp=0039845470&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039845470&partnerID=8YFLogxK

M3 - Article

VL - 46

SP - 215

EP - 230

JO - Algebra Universalis

JF - Algebra Universalis

SN - 0002-5240

IS - 1-2

ER -