Describing Ideals of Endomorphism Rings

Goldsmith, Brendan; Pabst, Simone

doi:10.33232/bims.0039.14.25

Irish Math. Soc. Bull.

1997

DOI: 10.33232/bims.0039.14.25

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Describing Ideals of Endomorphism Rings

Brendan Goldsmith¹,

Simone Pabst²

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2019

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Centrally stable algebras

Brešar

Gogić

2019

Journal of Algebra

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We define an algebra A to be centrally stable if, for every epimorphism ϕ from A to another algebra B, the center Z(B) of B is equal to ϕ(Z(A)), the image of the center of A. After providing some examples and basic observations, we consider in somewhat greater detail central stability in tensor products of algebras, and finally establish our main result which states that a finite-dimensional unital algebra A over a perfect field F is centrally stable if and only if A is isomorphic to a direct product of algebras of the form Ci ⊗F i Ai, where Fi is a field extension of F , Ci is a commutative Fi-algebra, and Ai is a central simple Fi-algebra.

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Centrally stable algebras

Brešar

Gogić

2019

Journal of Algebra

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show abstract

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Describing Ideals of Endomorphism Rings

Cited by 1 publication

References 4 publications

Centrally stable algebras

Centrally stable algebras

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