We will show that the bricks (of Bosbach) and the pseudo MV-algebras are each term equivalent to the class of semigroups with a pair of unary operations ^ and ˘ satisfying the equations: (âa)^b = b = b(aă)˘ and a($$ \hat b $$ a)˘ = (bă)^b and also show that a brick is an interval [0, u] of the positive cone of a unital lattice ordered group. We further extend the notion of implications to a pseudo MV-algebra and study the algebra of such implications.
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Open AccessBricks and pseudo MV-algebras are equivalent26. März 2008
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