• Corpus ID: 119289472

Proatomic modular ortholattices: representation and equational theory

@article{Herrmann2015ProatomicMO,
  title={Proatomic modular ortholattices: representation and equational theory},
  author={Christian Herrmann and Michael S. Roddy},
  journal={arXiv: Rings and Algebras},
  year={2015}
}
We study modular ortholattices in the variety generated by the finite dimensional ones from an equational and geometric point of view. We relate this to coordinatization results. 
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References

SHOWING 1-10 OF 70 REFERENCES
A note on the equational theory of modular ortholattices
Abstract. We prove that every atomic modular ortholattice is in the variety generated by its finite dimensional members.
A Finitely Generated Modular Ortholattice
Abstract We discuss [2] of the same title and offer an alternative example. This example is a subalgebra of the ortholattice of closed subspaces of separable real Hilbert space.
Varieties of modular ortholattices
The bottom of the lattice of varieties of modular ortholattices is described. The theorem that is proved is;THEOREM. Every variety of modular ortholattices which is different from all theMOn, 0≤n≤ω,
On the arithmetic of projective coordinate systems
A complete list of subdirectly irreducible modular (Arguesian) lattices generated by a frame of order n > 4 (n > 3) is given. Also, it is shown that a modular lattice variety containing the rational
Orthomodularity in infinite dimensions; a theorem of M. Solèr
Maria Pia Soler has recently proved that an orthomodular form that has an infinite orthonormal sequence is real, complex, or quaternionic Hilbert space. This paper provides an exposition of her
The coordinatization of Arguesian lattices
We show that the auxiliary planar ternary ring of an n-frame in an Arguesian lattice, n > 3, is indeed an associative ring with unit. The addition of two weak necessary conditions allows us to
On the Word Problem for Orthocomplemented Modular Lattices
  • M. Roddy
  • Mathematics
    Canadian Journal of Mathematics
  • 1989
In [16] Freese showed that the word problem for the free modular lattice on 5 generators is unsolvable. His proof makes essential use of Mclntyre's construction of a finitely presented field with
COMPLEMENTED MODULAR LATTICES
1.1 This paper gives a lattice theoretic investigation of “finiteness“ and “continuity of the lattice operations” in a complemented modular lattice. Although we usually assume that the lattice is
On Rings with Involution
  • I. Herstein
  • Mathematics
    Canadian Journal of Mathematics
  • 1974
In this note we prove some results which assert that under certain conditions the involution on a prime ring must satisfy a form of positive definiteness. As a consequence of the first of our
Complemented modular lattices and projective spaces of infinite dimension
Garrett Birkhoff [1](1) has shown that every complemented modular lattice of finite dimension is the direct union of lattices associated with projective geometries of finite dimension. The present
...
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