Subring structures in C(X) defined by absolute values

• Mohammad Ali Siavoshi ^[1]
  1. [1] University of Ahvaz, Irán
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 27, Nº. 1, 2026
• Idioma: inglés
• DOI: 10.4995/agt.24082
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we introduce and study two new classes of subrings of C(X): normclosed subrings and norm-reflecting subrings. A subring R ⊆ S ⊆ C(X) is said to be norm-closed if for every f ∈ S , the function | f | ∈ S ; it is norm-reflecting if | f | ∈ S implies f ∈ S . These concepts are inspired by the lattice structure ofC(X), particularly the operation of taking absolute values. We provide characterizations of norm-closed (norm-reflecting) subrings. Several examples and counterexamples are presented to illustrate the distinctions and connections between these classes.

• Referencias bibliográficas
  • F. Azarpanah, M. Namdari, and A. R. Olfati, On subrings of the form I +R of C(X), J. Commut. Algebra 11, no. 4 (2019), 479–509.
  • S. Ansari, M. Namdari, and M. A. Siavoshi, On algebraic subrings of rings of continuous functions, in preparation.
  • F. Azarpanah and E. Ghashghaei, Norm-closed and norm-reflecting ideals in rings of continuous functions, J. Algebra Appl. (2026), 2650073.
  • M. Ghadermazi, O. A. S. Karamzadeh, and M. Namdari, C(X) versus its functionally countable subalgebra, Bull. Iran Math. Soc. 45 (2019), 173–187.
  • M. Ghadermazi, O. A. S. Karamzadeh, and M. Namdari, On the functionally countable subalgebra of C(X), Rend. Semin. Mat. Univ. Padova 129 (2013),...
  • L. Gillman and M. Jerison, Rings of continuous functions, The University Series in Higher Math., Van Nostrand, Princeton, N. J., 1960.
  • L. Gillman and C. W. Kohls, Convex and pseudoprime ideals in rings of continuous functions, Math. Z. 72 (1959/60), 399–409.
  • L. D. Nel and D. Riordan, Note on a subalgebra of C(X), Canadian Mathematical Bulletin 15 (1972), 607–608.