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Journals / International Electronic Journal of Algebra / 2012 / Volume: 12 Issue: 12

ON GENERALIZED CODERIVATIONS

Atsushi Nakajima
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Publication Date
2012-12-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Nakajima, Weakly separable polynomials (in preparation), and give related examples of coseparable coalgebras.

📌 3 Key Takeaways

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Objective & Hypothesis:A) be a coalgebra (resp. algebra) over a commutative ring R and M (resp.
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Key Findings & Data:Math., 2(3) (1999), 345-352, by A.
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Conclusion & Impact:Nakajima, Weakly separable polynomials (in preparation), and give related examples of coseparable coalgebras.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:derivation · generalized derivation · coderivation

Abstract

Let C (resp. A) be a coalgebra (resp. algebra) over a commutative ring R and M (resp. N) a C-bicomodule (resp. an A-bimodule). We define a dual notion of a generalized derivation from A to N in the sense of the paper On categorical properties of generalized derivations, Sci. Math., 2(3) (1999), 345-352, by A. Nakajima, which we call a generalized coderivation from M to C. We give some elementary properties of generalized coderivations and discuss the relations of the set of generalized coderivations gCoder(M, C) between the set of generalized derivations gDer(C∗, M∗) for their dual algebra C∗ and module M∗. Using these coderivations, we define a notion of a weakly coseparable coalgebra which is a dual notion of a weakly separable algebra defined in the paper of N. Hamaguchi and A. Nakajima, Weakly separable polynomials (in preparation), and give related examples of coseparable coalgebras.

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Cite This Article

Nakajima, A. (2012). ON GENERALIZED CODERIVATIONS. International Electronic Journal of Algebra, Volume: 12 Issue: 12. https://ajindex.com/articles/1588235

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References (13)

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