# Implication Zroupoids and Identities of Associative Type

29 Oct 2017 Cornejo Juan M. Sankappanavar Hanamantagouda P.

An algebra $\mathbf A = \langle A, \to, 0 \rangle$, where $\to$ is binary and $0$ is a constant, is called an implication zroupoid ($\mathcal I$-zroupoid, for short) if $\mathbf A$ satisfies the identities: $(x \to y) \to z \approx [(z' \to x) \to (y \to z)']'$ and $0'' \approx 0$, where $x' : = x \to 0$, and $\mathcal I$ denotes the variety of all $\mathcal I$-zroupoids. An $\mathcal I$-zroupoid is symmetric if it satisfies $x'' \approx x$ and $(x \to y')' \approx (y \to x')'$... (read more)

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