Derya KESKİN TÜTÜNCÜ, Yosuke KURATOMI, Yoshiharu SHIBATA

2910

On image summand coinvariant modules and kernel summand invariant modules

On image summand coinvariant modules and kernel summand invariant modules

In this paper we introduce the concept of im-summand coinvariance and im-small coinvariance; that is, amodule M over a right perfect ring is said to be im-summand (im-small) coinvariant if, for any endomorphism φ of Psuch that Imφ is a direct summand (a small submodule) of P , φ(ker ) ker , where (P; ) is the projective cover ofM. We first give some fundamental properties of im-summand coinvariant modules and im-small coinvariant modules,and we prove that, for modules M and N over a right perfect ring such that N is a small epimorphic image of M, Mis N -im-summand coinvariant if and only if M is (im-coclosed) N -projective. Moreover, we introduce ker-summandinvariance and ker-essential invariance as the dual concept of im-summand coinvariance and im-small coinvariance,respectively, and show that, for modules M and N such that N is isomorphic to an essential submodule of M, M isN -ker-summand invariant if and only if M is (ker-closed) N -injective.
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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: Yılda 6 Sayı
  • Yayıncı: TÜBİTAK
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