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algebra universalis

, Volume 50, Issue 2, pp 231–257 | Cite as

When an algebraic frame is regular

  • Jorge Martinez
  • Eric R. Zenk
Original Paper

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 \( c^{\bot\bot} \), with c compact, is complemented. With a mild assumption on L, each \( c^{\bot} \), with c compact, is regular precisely when \( p \bigvee q = 1 \) 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.

Mathematics Subject Classification (2000):

06D22; 06B35, 06F20, 06F25. 

Keywords:

Algebraic frame regular frames compact splitting property latticeordered group f-ring 

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Copyright information

© Birkhäuser-Verlag Basel 2003

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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