A class of multiplicative lattices

Tiberiu Dumitrescu; Mihai Epure

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 2, page 591-601
  • ISSN: 0011-4642

Abstract

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We study the multiplicative lattices which satisfy the condition for all . Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group or . A sharp lattice localized at its maximal elements are totally ordered sharp lattices. The converse is true if has finite character.

How to cite

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Dumitrescu, Tiberiu, and Epure, Mihai. "A class of multiplicative lattices." Czechoslovak Mathematical Journal 71.2 (2021): 591-601. <http://eudml.org/doc/298202>.

@article{Dumitrescu2021,
abstract = {We study the multiplicative lattices $L$ which satisfy the condition $ a=(a :(a: b))(a:b) $ for all $a,b\in L$. Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group $\mathbb \{Z\}$ or $\mathbb \{R\}$. A sharp lattice $L$ localized at its maximal elements are totally ordered sharp lattices. The converse is true if $L$ has finite character.},
author = {Dumitrescu, Tiberiu, Epure, Mihai},
journal = {Czechoslovak Mathematical Journal},
keywords = {multiplicative lattice; Prüfer lattice; Prüfer integral domain},
language = {eng},
number = {2},
pages = {591-601},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A class of multiplicative lattices},
url = {http://eudml.org/doc/298202},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Dumitrescu, Tiberiu
AU - Epure, Mihai
TI - A class of multiplicative lattices
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 2
SP - 591
EP - 601
AB - We study the multiplicative lattices $L$ which satisfy the condition $ a=(a :(a: b))(a:b) $ for all $a,b\in L$. Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group $\mathbb {Z}$ or $\mathbb {R}$. A sharp lattice $L$ localized at its maximal elements are totally ordered sharp lattices. The converse is true if $L$ has finite character.
LA - eng
KW - multiplicative lattice; Prüfer lattice; Prüfer integral domain
UR - http://eudml.org/doc/298202
ER -

References

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