• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.85-90
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• 1991

In this article we introduce the readers to the theory of Carlitz modules which are rank one Drinfeld modules. The main point is the striking similarities between cyclotomic number fields and Carlitz modules.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.251-257
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• 1995

In the catagory of t-modules the Carlitz module C plays the role of $G_m$ in the category of group schemes. For a finite t-module G which corresponds to a finite group scheme, Taguchi [T] showed that Hom (G, C) is the "right" dual in the category of finite- t-modules which corresponds to the Cartier dual of a finite group scheme. In this paper we show that for Drinfeld modules (i.e., t-modules of dimension 1) of rank 2 there is a natural way of defining its dual by using the extension of drinfeld module by the Carlitz module which is in the same vein as defining the dual of an abelian varietiey by its $G_m$-extensions. Our results suggest that the extensions are the right objects to define the dual of arbitrary t-modules.t-modules.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.25-38
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• 2013

In this paper we compute the resultants of the Carlitz cyclotomic polynomials and then we address two applications to the setting of the Carlitz module.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.743-749
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• 1998

On the group of all extensions of elliptic modules by the Carlitz module we define Frobenius map and by using a concrete description of the extension group we give an explicit description of the Frobenius map.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.361-367
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• 1994

An elliptic module is an analogue of an elliptic curve over a function field [D]. The dual of an elliptic curve E is represented by Ext(E, $G_{m}$) and the Cartier dual of an affine group scheme G is represented by Hom(G, G$G_{m}$). In the category of elliptic modules the Carlitz module C plays the role of $G_{m}$. Taguchi [T] showed that a notion of duality of a finite t-module can be represented by Hom(G, C) in a suitable category. Our computation shows that the Ext-group as it stands is rather too "big" to represent a dual of an elliptic module.(omitted)