Naslov
Centrally Stable Algebras

Autori
Brešar, Matej ; Gogić, Ilja

Izvornik
Journal of algebra (0021-8693) 537 (2019); 79-97

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Centrally stable algebra ; centrally stable element ; center ; radical ; tensor product of algebras ; finite-dimensional algebra

Sažetak
We define an algebra $A$ to be centrally stable if, for every epimorphism $\varphi$ from $A$ to another algebra $B$, the center $Z(B)$ of $B$ is equal to $\varphi(Z(A))$, 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 $C_i\otimes_{; ; ; ; F_i}; ; ; ; A_i$, where $F_i$ is a field extension of $F$, $C_i$ is a commutative $F_i$- algebra, and $A_i$ is a central simple $F_i$- algebra.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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