AI 中文总结
本文研究实值域代数范数的乘性等性质在基域扩张下的保持问题，得到对应精确判据并推广了Poineau的相关结果。
AI 中文摘要
完备非阿基米德域上巴拿赫代数上的通用（或几何）乘性范数，被Berkovich用于其非阿基米德几何学研究，后由Poineau进行了详细研究。本文更深入地研究实值域上代数的范数的乘性、谱性与谱乘性在基域扩张下保持的问题，得到了与经典几何不可约性及约化理论极为相似的精确判据，尤其在若干方面推广了Poineau的结果。
英文摘要
Universally (or geometrically) multiplicative norms on Banach algebras over complete non-archimedean fields were used by Berkovich in his works on non-archimedean geometry, and later they were studied in some detail by Poineau. In this paper, we perform a more thorough study of the question when multiplicativity, spectrality and spectral multiplicativity of norms on algebras over real valued fields are preserved by ground field extensions. We obtain precise criteria quite analogous to the classical theory of geometric irreducibility and reducedness. In particular, we generalize the results of Poineau in a few aspects.
Comments15 pages, first version, comments are welcome
