Category:B-Algebras

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This category contains results about B-Algebras.
Definitions specific to this category can be found in Definitions/B-Algebras.


Let $\struct {X, \circ}$ be an algebraic structure.

Then $\struct {X, \circ}$ is a $B$-algebra if and only if:

\((\text {AC})\)   $:$     \(\displaystyle \forall x, y \in X:\) \(\displaystyle x \circ y \in X \)             
\((\text A 0)\)   $:$   \(\displaystyle \exists 0 \in X \)             
\((\text A 1)\)   $:$     \(\displaystyle \forall x \in X:\) \(\displaystyle x \circ x = 0 \)             
\((\text A 2)\)   $:$     \(\displaystyle \forall x \in X:\) \(\displaystyle x \circ 0 = x \)             
\((\text A 3)\)   $:$     \(\displaystyle \forall x, y, z \in X:\) \(\displaystyle \paren {x \circ y} \circ z = x \circ \paren {z \circ \paren {0 \circ y} } \)