单一岩浆作用

Nelson Martins-Ferreira
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引用次数: 0

摘要

我们为单元岩浆引入了一个新的作用概念,便于对这一代数结构中的各种分裂扩展进行分类。我们的方法拓展了格兰、雅内利泽和索布拉尔最近对单位岩浆的分裂扩展和半直接积的研究。在他们的研究基础上,我们探讨了中间对象不一定与其末端对象的笛卡尔积保持双射对应关系的分裂扩展。虽然这种现象在群或通用代数的任何共轭半阿贝尔种类中都观察不到,但它与通过弱施莱尔扩展和某些奇异的非共轭代数(如半左环)在单子中发现的情况有相似之处。我们的工作旨在为理解单元岩浆中的分裂扩展做出贡献,并为在更广义的背景下对分类性质进行潜在抽象提供有价值的见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Unitary magma actions
We introduce a novel concept of action for unitary magmas, facilitating the classification of various split extensions within this algebraic structure. Our method expands upon the recent study of split extensions and semidirect products of unitary magmas conducted by Gran, Janelidze, and Sobral. Building on their research, we explore split extensions in which the middle object does not necessarily maintain a bijective correspondence with the Cartesian product of its end objects. Although this phenomenon is not observed in groups or any associative semiabelian variety of universal algebra, it shares similarities with instances found in monoids through weakly Schreier extensions and certain exotic non-associative algebras, such as semi-left-loops. Our work seeks to contribute to the comprehension of split extensions in unitary magmas and may offer valuable insights for potential abstractions of categorical properties in more general contexts.
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