# Category:B-Algebras

This category contains results about B-Algebras.

Definitions specific to this category can be found in Definitions/B-Algebras.

Let $\left({X, \circ}\right)$ be an algebraic structure.

Then $\left({X, \circ}\right)$ is a **$B$-algebra** if and only if:

\((AC)\) | $:$ | \(\displaystyle \forall x, y \in X:\) | \(\displaystyle x \circ y \in X \) | |||||

\((A0)\) | $:$ | \(\displaystyle \exists 0 \in X \) | ||||||

\((A1)\) | $:$ | \(\displaystyle \forall x \in X:\) | \(\displaystyle x \circ x = 0 \) | |||||

\((A2)\) | $:$ | \(\displaystyle \forall x \in X:\) | \(\displaystyle x \circ 0 = x \) | |||||

\((A3)\) | $:$ | \(\displaystyle \forall x,y,z \in X:\) | \(\displaystyle \left({x \circ y}\right) \circ z = x \circ \left({z \circ \left({0 \circ y}\right)}\right) \) |

## Pages in category "B-Algebras"

The following 24 pages are in this category, out of 24 total.

### B

- B-Algebra Identity: 0(0x)=x
- B-Algebra Identity: x (y z) = (x (0 z)) y
- B-Algebra Identity: xy = 0 iff x = y
- B-Algebra Identity: xy=x(0(0y))
- B-Algebra Induced by Group Induced by B-Algebra
- B-Algebra Induces Group
- B-Algebra is Commutative iff x(xy)=y
- B-Algebra is Left Cancellable
- B-Algebra is Quasigroup
- B-Algebra is Right Cancellable
- B-Algebra Power Law
- B-Algebra Power Law with Zero