ON CONTINUOUS AND ADJOINT MORPHISMS BETWEEN NON-COMMUTATIVE PRIME SPECTRA

Proceedings of the Edinburgh Mathematical Society

Edward S. Letzter¹ 

关键词: Primary 16D25;    16S20;    non-commutative ring;    ring extension;    prime ideal;   

DOI  :  10.1017/S0013091504000628

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We study topological properties of the correspondence of prime spectra associated with a non-commutative ring homomorphism $Rightarrow S$. Our main result provides criteria for the adjointness of certain functors between the categories of Zariski closed subsets of $spec R$ and $spec S$; these functors arise naturally from restriction and extension of scalars. When $R$ and $S$ are left Noetherian, adjointness occurs only for centralizing and ‘nearly centralizing’ homomorphisms.

【 授权许可】

Unknown