Trigintaduonion

Trigintaduonions
Symbol	${\displaystyle \mathbb {T} }$
Type	Hypercomplex algebra
Units	e0, ..., e31
Multiplicative identity	e0
Main properties	Power associativity Distributivity
Common systems
${\displaystyle \mathbb {N} }$ Natural numbers ${\displaystyle \mathbb {Z} }$ Integers ${\displaystyle \mathbb {Q} }$ Rational numbers ${\displaystyle \mathbb {R} }$ Real numbers ${\displaystyle \mathbb {C} }$ Complex numbers ${\displaystyle \mathbb {H} }$ Quaternions Less common systems ${\displaystyle \mathbb {O} }$ Octonions ${\displaystyle \mathbb {S} }$ Sedenions ${\displaystyle \mathbb {T} }$ Trigintaduonions

In abstract algebra, the trigintaduonions, also known as the 32-ions, 32-nions, 2⁵-nions, or sometimes pathions (${\displaystyle \mathbb {P} }$),^[1][2] form a 32-dimensional noncommutative and nonassociative algebra over the real numbers,^[3][4] usually represented by the capital letter T, boldface T or blackboard bold ${\displaystyle \mathbb {T} }$.^[2]