When an algebraic frame is regular

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.