On the networks of large embeddings

Aslan Khalifa T., Khalıfa M. K. M. I., Székely G.

ALGEBRA UNIVERSALIS, vol.85, no.3, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 85 Issue: 3
  • Publication Date: 2024
  • Doi Number: 10.1007/s00012-024-00862-8
  • Journal Name: ALGEBRA UNIVERSALIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Keywords: Large embeddings, Generator distance, Monounary algebras
  • Istanbul Medipol University Affiliated: Yes

Abstract

We define a special network that exhibits the large embeddings in any class of similar algebras. With the aid of this network, we introduce a notion of distance that conceivably counts the minimum number of dissimilarities, in a sense, between two given algebras in the class in hand; with the possibility that this distance may take the value ∞. We display a number of inspirational examples from different areas of algebra, e.g., group theory and monounary algebras, to show that this research direction can be quite remarkable.