When an algebraic frame is regular |
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Authors: | Email author" target="_blank">Jorge?MartinezEmail author Eric?R?Zenk |
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Institution: | (1) Department of Mathematics, University of Florida, P.O. Box 118105, 32611-8105 Gainesville, FL, USA |
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Abstract: | It is shown that an algebraic frame L is regular if
and only if its compact
elements are complemented. More generally, it is shown that each pseudocomplemented
element is regular if and only if each
, with c compact, is complemented.
With a mild assumption on L, each
, with c compact, is regular precisely
when
for any
two minimal primes p and q
of L. These results are then interpreted in various frames of
subobjects of lattice-ordered groups and f-rings. |
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Keywords: | 06D22 06B35 06F20 06F25 |
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