대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제58권6호
  • /
  • Pages.1563-1567
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  • 2021
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A DECOMPOSITION THEOREM FOR UTUMI AND DUAL-UTUMI MODULES

  • Ibrahim, Yasser (Department of Mathematics Faculty of Science Cairo University and Department of Mathematics Faculty of Science Taibah University) ;
  • Yousif, Mohamed (Department of Mathematics The Ohio State University)
  • 투고 : 2021.02.01
  • 심사 : 2021.07.12
  • 발행 : 2021.11.30
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초록

We show that if M is a Utumi module, in particular if M is quasi-continuous, then M = Q ⊕ K, where Q is quasi-injective that is both a square-full as well as a dual-square-full module, K is a square-free module, and Q & K are orthogonal. Dually, we also show that if M is a dual-Utumi module whose local summands are summands, in particular if M is quasi-discrete, then M = P ⊕ K where P is quasi-projective that is both a square-full as well as a dual-square-full module, K is a dual-square-free module, and P & K are factor-orthogonal.

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참고문헌

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