On the rhomboidal heredity in ideal lattices

Ladislav Beran

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 4, page 723-726
  • ISSN: 0010-2628

Abstract

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We show that the class of principal ideals and the class of semiprime ideals are rhomboidal hereditary in the class of modular lattices. Similar results are presented for the class of ideals with forbidden exterior quotients and for the class of prime ideals.

How to cite

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Beran, Ladislav. "On the rhomboidal heredity in ideal lattices." Commentationes Mathematicae Universitatis Carolinae 33.4 (1992): 723-726. <http://eudml.org/doc/247410>.

@article{Beran1992,
abstract = {We show that the class of principal ideals and the class of semiprime ideals are rhomboidal hereditary in the class of modular lattices. Similar results are presented for the class of ideals with forbidden exterior quotients and for the class of prime ideals.},
author = {Beran, Ladislav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {rhomboidal heredity; principal ideal; semiprime ideal; modular lattice; quotient; allele; relatively complemented lattice; weakly perspective; weakly projective quotients; allele; relatively complemented lattice; principal ideals; semiprime ideals; modular lattices; ideals with forbidden exterior quotients; prime ideals},
language = {eng},
number = {4},
pages = {723-726},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the rhomboidal heredity in ideal lattices},
url = {http://eudml.org/doc/247410},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Beran, Ladislav
TI - On the rhomboidal heredity in ideal lattices
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 4
SP - 723
EP - 726
AB - We show that the class of principal ideals and the class of semiprime ideals are rhomboidal hereditary in the class of modular lattices. Similar results are presented for the class of ideals with forbidden exterior quotients and for the class of prime ideals.
LA - eng
KW - rhomboidal heredity; principal ideal; semiprime ideal; modular lattice; quotient; allele; relatively complemented lattice; weakly perspective; weakly projective quotients; allele; relatively complemented lattice; principal ideals; semiprime ideals; modular lattices; ideals with forbidden exterior quotients; prime ideals
UR - http://eudml.org/doc/247410
ER -

References

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  1. Beran L., Orthomodular Lattices (Algebraic Approach), Reidel Dordrecht (1985). (1985) Zbl0558.06008MR0784029
  2. Beran L., On semiprime ideals in lattices, J. Pure Appl. Algebra 64 (1990), 223-227. (1990) Zbl0703.06003MR1061299
  3. Grätzer G. and Schmidt E.T., On ideal theory for lattices, Acta Sci. Math. 19 (1958), 82-92. (1958) MR0095795
  4. Rav Y., Semiprime ideals in general lattices, J. Pure Appl. Algebra 56 (1989), 105-118. (1989) Zbl0665.06006MR0979666

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