##### Department of Mathematics,

University of California San Diego

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### Algebra Seminar

## Adam Chapman

#### Michigan State University

## Linkage of p-algebras of prime degree

##### Abstract:

Quaternion algebras contain quadratic field extensions of the center. Given two algebras, a natural question to ask is whether they share a common field extension. This gives us an idea of how closely related those algebras are to one another. If the center is of characteristic 2 then those extensions divide into two types - the separable type and the inseparable type. It is known that if two quaternion algebras share an inseparable field extension then they also share a separable field extension and that the converse is not true. We shall discuss this fact and its generalization to p-algebras of arbitrary prime degree.

### March 3, 2016

### 2:00 PM

### AP&M 7321

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