Primitivity preserving endomorphisms of free groups

有限生成自由半群自同态的不可约性

Irreducibility of Endomorphisms of Finitely Generated Free Semigroups

本文研究有限生成自由半群自同态的不可约性，引入素性概念，给出保秩自同态可约与不可约的判别条件，并分析分解的非唯一性及关联矩阵的应用。

Primitive Words, Free Factors and Measure Preservation

Let F_k be the free group on k generators. A word w \in F_k is called primitive if it belongs to some basis of F_k. We investigate two criteria for primitivity, and consider more generally, subgroups of F_k which are free factors. The first criterion is graph-theoretic and uses Stallings core graphs: given subgroups of finite rank H \le J \le F_k we present a simple procedure to determine whether H is a free factor of J. This yields, in particular, a procedure to determine whether a given element in F_k is primitive. Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from t…

将环表示为阿贝尔群的自同态环

Representing a ring as the endomorphism ring of an abelian group

本文在ZFC中通过结合κ-框架与Shelah超黑箱，构造了自同态环同构于给定环的μ^+-自由模，部分解决了Göbel和Trlifaj关于环表示的问题。

伴随Chevalley群的Sha-刚性

Sha-rigidity of adjoint Chevalley groups of types $A_1$, $A_2$, $B_2$, $G_2$ over commutative rings

本文证明了在特定环上，A1、A2、B2和G2类型的伴随Chevalley群及其初等子群的局部内自同构是内自同构，从而这些群具有Sha-刚性。