Naslov
On the ideal structure of the tensor product of nearly simple algebras

Autori
Gogić, Ilja

Izvornik
Communications in algebra (0092-7872) 48 (2020), 5; 2248-2257

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

Ključne riječi
nearly simple algebra, tensor product of algebras, ideals

Sažetak
We define a unital algebra $A$ over a field $\mathbb{; ; F}; ; $ to be nearly simple if $A$ contains a unique non-trivial ideal $I_A$ such that $I_A^2 \neq \{; ; 0\}; ; $. If $A$ and $B$ are two nearly simple algebras, we consider the ideal structure of their tensor product $A \otimes B$. The obvious non-trivial ideals of $A \otimes B$ are: $$I_A \otimes I_B, \quad I_A \otimes B, \quad A \otimes I_B, \quad \mbox{; ; and}; ; \quad I_A \otimes B + A \otimes I_B.$$ The purpose of this paper is to characterize when are all non-trivial ideals of $A \otimes B$ of the above form.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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