ON GENERALIZED CODERIVATIONS

Atsushi NAKAJİMA

Article Details

ON GENERALIZED CODERIVATIONS

Authors:

Atsushi NAKAJİMA

Publisher:

Abdullah HARMANCI

Journal:

International Electronic Journal of Algebra 2012 Vol.12 Issue 12, pp.37-52

Document Type:

Article

Publication Date:

11/2012

Document Language:

Turkish

Document ID (Org No.):

2000718257

Frequency:

Monthly

eISSN:

1306-6048

pISSN:

1306-6048

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.

Article Details

ON GENERALIZED CODERIVATIONS

Authors: Atsushi NAKAJİMA

Publisher: Abdullah HARMANCI

Journal: International Electronic Journal of Algebra 2012 Vol.12 Issue 12, pp.37-52

Document Type: Article

Publication Date: 11/2012

Document Language: Turkish

Document ID (Org No.): 2000718257

Frequency: Monthly

eISSN: 1306-6048

pISSN: 1306-6048

Issues

Authors:

Atsushi NAKAJİMA

Publisher:

Abdullah HARMANCI

Journal:

International Electronic Journal of Algebra 2012 Vol.12 Issue 12, pp.37-52

Document Type:

Article

Publication Date:

11/2012

Document Language:

Turkish

Document ID (Org No.):

2000718257

Frequency:

Monthly

eISSN:

1306-6048

pISSN:

1306-6048