On rigid Hermitean lattices, II

Ana Cecilia de la Maza; Remo Moresi

doi:10.4067/S0719-06462018000100065

DOI:

https://doi.org/10.4067/S0719-06462018000100065

Abstract

We study the indexed Hermitean lattice of type 0 generated by a single element a subjected to the relation a â‰¤ b^âŠ¥ âˆ§ bb^âŠ¥= 0. We prove that it is finite, provided that two crucial indices are finite. We show that index relations imply algebraic relations and describe the lattice by means of its subdirectly irreducible factors. We finally use the results to confirm a conjecture appeared in 2000.

Keywords

Lattices , semilattices , modular lattices , Hermitean lattices , orthogonal geometry

Ana Cecilia de la Maza Departamento de Matemática y Estadística, Universidad de la Frontera, Temuco, Chile.
Remo Moresi Cerfim, cp 1132, 6601 Locarno, Switzerland.

Pages: 65–78
Date Published: 2018-10-19
Vol. 20 No. 1 (2018)

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