New results on free and simple hypermodules


Türkmen E., Kahriman F., Aydın Y.

AIMS Mathematics, cilt.11, sa.6, ss.18202-18221, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 6
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3934/math.2026740
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.18202-18221
  • Anahtar Kelimeler: free hypermodule, normal projective (injective) hypermodule, simple hypermodule
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

In this paper, we investigate the relationship between free hypermodules and normal projective hypermodules. In particular, we prove that every cyclic free R-hypermodule is normal projective and establish a criterion characterizing the normal projectivity of subhypermodules of the free hypermodule H(R), where R is a hyperring. In addition, by means of quotient hypermodule constructions, we provide an example of a free hypermodule arising from a free module. Furthermore, we study the normal injectivity of simple hypermodules and obtain a fundamental characterization of hyperrings whose simple hypermodules are normal injective.