AI 中文总结
本文推广Rump的根基环与括号对应关系，利用近环定义拓扑右斜括号，其乘法群可自然对应Nottingham群等典型群，实现了相关代数结构的拓展应用。
AI 中文摘要
本文将Rump关于根基环与括号的对应关系推广到更一般的情形，利用一类合适的近环。给定带有乘法单位元的右近环(R,+,∘)，我们定义一个新运算，该运算生成一个幺半群。在通过滤子表达的自然相容性条件下，这个幺半群成为拓扑群，进而得到拓扑右斜括号。该推广可还原根基环括号，并成功应用于复合映射构成的近环。我们给出若干显式应用，证明Nottingham群、三角函数群、任意群的迭代 wreath 积、自由幂零群的IA-自同构群自然作为这类拓扑斜括号的乘法群出现。
英文摘要
This paper adapts Rump's correspondence between radical rings and braces to a more general setting, utilizing a suitable class of near-rings. Given a right near-ring $(R,+,\circ)$ with a multiplicative identity, we define a new operation that yields a monoid. Under natural compatibility conditions expressed via a filtration, this monoid becomes a topological group, yielding a topological right skew brace. This generalization recovers radical-ring braces and successfully applies to near-rings of maps under composition. We provide several explicit applications, demonstrating that the Nottingham group, groups of triangular functions, iterated wreath products of arbitrary groups, and groups of IA-automorphisms of free nilpotent groups naturally arise as multiplicative groups of such topological skew braces.
