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Reports on Mathematical Logic

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No. 42

James G. RAFTERY

On the Variety Generated by Involutive Pocrims
A b s t r a c t. An *involutive pocrim* (a.k.a. an $L_0$-*algebra)* is
a residuated integral partially ordered commutative monoid with an involution operator, considered
as an algebra. It is proved that the variety generated by all involutive pocrims satisfies no nontrivial
idempotent Maltsev condition. That is, no nontrivial $\langle\wedge,\vee,\circ\rangle$-equation holds in the congruence
lattices of all involutive pocrims. This strengthens a theorem of A. Wro\'{n}ski. The
result survives if we restrict the generating class to *totally ordered* involutive pocrims.

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