Bricks and pseudo MV-algebras are equivalent

Year, pages: 2008, 131 - 142

We will show that the bricks (of Bosbach) and the pseudo \mbox{MV-al} ge bras are each term equivalent to the class of semigroups with a pair of unary operations $\hat{} $ and $\check{} $ satisfying the equations: $(\hat{a}a)\hat{} b = b = b (a \check{a}) \check{} $ and $a (\hat{b}a) \check{} =(b \check{a})\hat{} b$ 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.

Subrahmanyam, N. 2008. Bricks and pseudo MV-algebras are equivalent. In Mathematica Slovaca, vol. 58, no.2, pp. 131-142. 0139-9918.

Subrahmanyam, N. (2008). Bricks and pseudo MV-algebras are equivalent. Mathematica Slovaca, 58(2), 131-142. 0139-9918.