Category:Definitions/B-Algebras
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This category contains definitions related to B-Algebras.
Related results can be found in Category:B-Algebras.
Let $\struct {X, \circ}$ be an algebraic structure.
$\struct {X, \circ}$ is a $B$-algebra if and only if $\struct {X, \circ}$ satisfies the $B$-algebra axioms:
\((\text {AC})\) | $:$ | \(\ds \forall x, y \in X:\) | \(\ds x \circ y \in X \) | ||||||
\((\text A 0)\) | $:$ | \(\ds \exists 0 \in X \) | |||||||
\((\text A 1)\) | $:$ | \(\ds \forall x \in X:\) | \(\ds x \circ x = 0 \) | ||||||
\((\text A 2)\) | $:$ | \(\ds \forall x \in X:\) | \(\ds x \circ 0 = x \) | ||||||
\((\text A 3)\) | $:$ | \(\ds \forall x, y, z \in X:\) | \(\ds \paren {x \circ y} \circ z = x \circ \paren {z \circ \paren {0 \circ y} } \) |
Pages in category "Definitions/B-Algebras"
The following 3 pages are in this category, out of 3 total.