ON ALMOST N-SIMPLE-PROJECTIVES

• Baba Yoshitomo

• Yamazaki Takeshi

抄録

The concept of almost N-projectivity is defined in [5] by M. Harada and A. Tozaki to translate the concept "lifting module" in terms of homomorphisms. In [6, Theorem 1] M. Harada defined a little weaker condition "almost N-simple-projecive" and gave the following relationship between them: For a semiperfect ring R and R-modules M and N of finite length, M is almost N-projective if and only if M is almost N-simple-projective. We remove the assumption "of finite length" and give the result in Theorem 5 as follows: For a semiperfect ring R, a finitely generated right R-module M and an indecomposable right R-module N of finite Loewy length, M is almost N-projective if and only if M is almost N-simple-projective. We also see that, for a semiperfect ring R, a finitely generated R-module M and an R-module N of finite Loewy length, M is N-simple-projective if and only if M is N-projective.

収録刊行物

• Mathematical Journal of Okayama University

  Mathematical Journal of Okayama University 53 (1), 101-109, 2011-01

  Department of Mathematics, Faculty of Science, Okayama University

キーワード

• ring
• module
• almot projective
• almost simple-projective

詳細情報

• CRID: 1390290699601621632
• NII論文ID: 120002693900
• NII書誌ID: AA00723502
• ISSN: 00301566
• DOI: 10.18926/mjou/41400
• Web Site: https://ousar.lib.okayama-u.ac.jp/41400
• 本文言語コード: en
• データソース種別:
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  • IRDB
  • CiNii Articles