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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 4

Two results on double crossed biproducts

Tianshui Ma(Henan Normal University)0000-0003-1275-7214
Bei Li(Henan Normal University)0000-0002-2449-7387
Sayfa
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Yayın Tarihi
2022-08-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Algebra Appl. 16 (4), 1760061, 2017] which induces a description of C ⋆ α H β ⋆ D C⋆αHβ⋆D similar to Majid double biproduct C ⋆ H ⋆ D C⋆H⋆D and also present some related structures.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let H H be an algebra with a distinguished element ε H ∈ H ∗ εH∈H∗ and C , D C,D two coalgebras.
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Temel Bulgular & Veri:Based on the construction of Brzeziński’s crossed coproduct, under some suitable conditions, we introduce a coassociative coalgebra C × G T H β R × D C×TGHRβ×D which is a more general two-sided coproduct structure including two-sided smash coproduct.
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Sonuç & Katkı:Algebra Appl. 16 (4), 1760061, 2017] which induces a description of C ⋆ α H β ⋆ D C⋆αHβ⋆D similar to Majid double biproduct C ⋆ H ⋆ D C⋆H⋆D and also present some related structures.
🔬Tür:Research Article
📍Kapsam:2017 Verileri
⚙️Değişkenler:crossed coproduct · Radford biproduct · double biproduct

Abstract

Let H H be an algebra with a distinguished element ε H ∈ H ∗ εH∈H∗ and C , D C,D two coalgebras. Based on the construction of Brzeziński’s crossed coproduct, under some suitable conditions, we introduce a coassociative coalgebra C × G T H β R × D C×TGHRβ×D which is a more general two-sided coproduct structure including two-sided smash coproduct. Necessary and sufficient conditions for C × G T H β R × D C×TGHRβ×D equipped with two-sided tensor product algebra C ⊗ H ⊗ D C⊗H⊗D to be a bialgebra (Hopf algebra) are provided. On the other hand, we obtain an improved version of the double crossed biproduct C ⋆ α H β ⋆ D C⋆αHβ⋆D in [An extended form of Majid's double biproduct, J. Algebra Appl. 16 (4), 1760061, 2017] which induces a description of C ⋆ α H β ⋆ D C⋆αHβ⋆D similar to Majid double biproduct C ⋆ H ⋆ D C⋆H⋆D and also present some related structures.

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Bu Makaleye Atıf Yap

Ma, T., Li, B. (2022). Two results on double crossed biproducts. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 4. https://doi.org/10.15672/hujms.997154

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Kaynakça (14)

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