Algebraically and geometrically closed of idempotents

Document Type : Full Length Article

Author

Department of Mathematics, Faculty of Mathematical Sciences, Farhangian University of Tehran, Iran

Abstract

Our aim in this article is to study algebraically and geometrically closed structures in a commutative ring with unity R. It is proved that the lattice of idempotents E of R is an algebraically closed lattice. We also show that if E is dense-in-itself, then E* is geometrically closed in Mod(T, A ). Finally, the relationship between an equicharacteristic regular local ring and an algebraically closed residue field is considered.

Keywords

Main Subjects


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Volume 10, Issue 3
September 2025
Pages 283-291
  • Receive Date: 30 March 2025
  • Revise Date: 09 May 2025
  • Accept Date: 26 June 2025
  • First Publish Date: 01 August 2025
  • Publish Date: 01 September 2025