On the generic polynomial of degree two algebras

https://www.ams.org/tran/1950-069-00/S0002-9947-1950-0038959-X/S0002-9947-1950-0038959-X.pdf

A theory of power-associative commutative algebras

The notions of the rank or principal polynomial of an associative algebra and the corresponding notions of trace and norm are classical. These notions have been generalized recently by the author ([13,I]) to apply to strictly power associative algebras, and we have renamed these concepts the generic minimal polynomial, trace and norm, since this terminology appears to be more in keeping with present day usage in analogous situations. In our paper we investigated the groups of linear transformations which preserve the norms in special central simple Jordan algebras. This applies to central simple associative algebras as a special case. In a later paper ([13, III]) we studied the norm preserving groups of exceptional central simple Jordan algebras. The groups obtained in this way are generalizations of the complex Lie group E 6 and include certain geometrically defined subgroups of the collineation groups of Cayley planes.

/pdf/generic-norm-of-an-algebra-2bhtcs0mff.pdf

Generic norm of an algebra

/pdf/new-results-on-power-associative-algebras-42d8ob7fc1.pdf

New results on power-associative algebras

/pdf/on-commutative-power-associative-algebras-of-degree-two-1ncyd45rn0.pdf

On the generic polynomial of degree two algebras

References

A theory of power-associative commutative algebras

Generic norm of an algebra

New results on power-associative algebras

On commutative power-associative algebras of degree two

Simple Power-Associative Algebras of Degree Two

Related Papers (5)

A note on complete intersections

Poisson brackets and two-generated subalgebras of rings of polynomials

Every curve on a nonsingular surface can be defined by two equations

Algebraic monoids whose nonunits are products of idempotents

Invariants of finite cyclic groups acting on generic matrices