关于Buchstaber–Rees“Frobenius n-同态”理论及其推广
On the Buchstaber--Rees theory of "Frobenius $n$-homomorphisms" and its generalization
AI总结：
本文综述了Buchstaber–Rees n-同态理论及其推广，提出以特征函数刻画交换环间线性映射的乘法性质，并由此引入p|q-同态新概念，简化了原有理论。
摘要：
本文是对我们所得Buchstaber–Rees n-同态理论及其推广结果的综述。简言之，我们关注的是交换环之间的一类线性映射，就乘法性质而言，这类映射可被描述为“环同态之后的下一个层次”。我们的主要工具是一种我们称之为“特征函数”的构造，其函数性质编码了所讨论线性映射的代数性质。也就是说，若特征函数是n次多项式，则该映射是Buchstaber–Rees意义下的n-同态，我们的方法大幅简化了他们的理论。若特征函数是不可约有理分式，其分子和分母的次数分别为p和q，我们就得到一个新的“p|q-同态”概念。p|q-同态的例子包括环同态的和与差。我们的构造受到我们早先在超代数/超几何中关于Berezinians和超外幂的结果的启发。
英文摘要：
This is a survey of our results on the theory of $n$-homomorphisms of Buchstaber--Rees and its generalization that we obtained. In short, we are concerned with classes of linear maps between commutative rings that can be described the "next level after ring homomorphisms" with respect to multiplicative properties. Our main tool is a construction which we call the "characteristic function" -- whose functional properties encode algebraic properties of a linear map in question. Namely, if the characteristic function is polynomial of degree $n$, the map is an $n$-homomorphism in the sense of Buchstaber--Rees, and our approach simplifies their theory substantially. If the characteristic function is an irreducible rational fraction with the numerator and denominator of degrees $p$ and $q$ respectively, we arrive at a new notion of a "$p|q$-homomorphism". Examples of $p|q$-homomorphisms are sums and differences of ring homomorphisms. Our construction is motivated by our earlier results in superalgebra/supergeometry concerning Berezinians and super exterior powers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
