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phi-beta-prime submodules

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Thawatchai Khumprapussorn at King Mongkut's Institute of Technology Ladkrabang
Thawatchai Khumprapussorn
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Abstract

R M R S(M) M φ : S(M) → S(M) ∪ {∅} P M φβ r ∈ R m ∈ M rm ∈ P \φ(P) r + r ∈ (P : M) m + m ∈ P φβ φβ β φβ R M R N M {r ∈ R | rM ⊆ N } (N : M) P M r ∈ R m ∈ M rm ∈ P r ∈ (P : M) m ∈ P 2 2 S(M) M φ : S(M) → S(M) ∪ {∅} φ(P) ⊆ P 2 φ φ φ2 P M φ r ∈ R m ∈ M rm ∈ P \φ(P) r ∈ (P : M) m ∈ P φ φ φ(N) = ∅ N M φ φ(N) = {0} N M φ φ(N) = (N : M)M N M φ φ φ φ 2 2 φ2 φβ β β φβ (G, +) H ⊆ G β(H) {h + h | h ∈ H} α(H) {h | h + h ∈ H} β(H) ⊆ H ⊆ α(H) I R α(I) β(I) R N M α(N) β(N) M P R M β M r ∈ R m ∈ M rm ∈ P r + r ∈ (P : M) m + m ∈ P
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The 24th Annual Meeting in Mathematics (AMM 2019)
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