Scholarlink

<p>In this paper, we define operations on preradicals in arbitrary abelian categories. We define idempotent preradicals and radicals. We prove that every adjoint pair between abelian categories induces a Galois connection between the corresponding ordered collections of preradicals. If the abelian categories are bicomplete, we construct alpha and omega preradicals and study their respective preservation under the Galois connection. If a bicomplete abelian category is in addition locally small, then the corresponding collection of preradicals is a complete lattice. The Galois connection induced by an adjoint pair between locally small bicomplete abelian categories preserves, respectively, idempotent preradicals and radicals.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Galois connections and preradicals in abelian categories

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月31日

查看全文
  • Rogelio Fernández-Alonso,
  • Janeth Magaña,
  • Martha Lizbeth Shaid Sandoval-Miranda,
  • Valente Santiago-Vargas

摘要

In this paper, we define operations on preradicals in arbitrary abelian categories. We define idempotent preradicals and radicals. We prove that every adjoint pair between abelian categories induces a Galois connection between the corresponding ordered collections of preradicals. If the abelian categories are bicomplete, we construct alpha and omega preradicals and study their respective preservation under the Galois connection. If a bicomplete abelian category is in addition locally small, then the corresponding collection of preradicals is a complete lattice. The Galois connection induced by an adjoint pair between locally small bicomplete abelian categories preserves, respectively, idempotent preradicals and radicals.