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Annulets and α-ideals in a distributive lattice

Published online by Cambridge University Press:  09 April 2009

William H. Cornish
William H. Cornish
Affiliation:
The Flinders University of South AustraliaBedford Park, South Australia 5042
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In a distributive lattice L with 0 the set of all ideals of the form (x]* can be made into a lattice A0(L) called the lattice of annulets of L. A 0(L) is a sublattice of the Boolean algebra of all annihilator ideals in L. While the lattice of annulets is no more than the dual of the so-called lattice of filets (carriers) as studied in the theory of l-groups and abstractly for distributive lattices in [1, section4] it is a useful notion in its own right. For example, from the basic theorem of [3] it follows that A 0(L) is a sublattice of the lattice of all ideals of L if and only if each prime ideal in L contains a unique minimal prime ideal.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 1 , February 1973 , pp. 70 - 77
Copyright
Copyright © Australian Mathematical Society 1973

References

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