Fully coprime comodules and fully coprime corings

Jawad Y. Abuhlail

doi:10.1007/s10485-006-9040-9

Fully coprime comodules and fully coprime corings

Jawad Y. Abuhlail^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Prime objects were defined as generalization of simple objects in the categories of rings (modules). In this paper we introduce and investigate what turns out to be a suitable generalization of simple corings (simple comodules), namely fully coprime corings (fully coprime comodules). Moreover, we consider several primeness notions in the category of comodules of a given coring and investigate their relations with the fully coprimeness and the simplicity of these comodules. These notions are applied then to study primeness and coprimeness properties of a given coring, considered as an object in its category of right (left) comodules.

Original language	English
Pages (from-to)	379-409
Number of pages	31
Journal	Applied Categorical Structures
Volume	14
Issue number	5-6
DOIs	https://doi.org/10.1007/s10485-006-9040-9
State	Published - Dec 2006

Bibliographical note

Funding Information:
Supported by King Fahd University of Petroleum and Minerals, Research Project # INT/296.

Funding Information:
Acknowledgements Many thanks for the referee for the careful reading of the paper and for his/her suggestions, which improved the paper. The author thanks also Prof Stefaan Caenepeel for inviting him to submit a paper to this special issue of the journal. The author is grateful to Prof Robert Wisbauer and to Christian Lomp for fruitful discussions on the subject. He thanks also Virginia Rodrigues for sending him preprints of [9]. The author is also grateful for the financial support and the excellent research facilities provided by KFUPM.

Keywords

Fully coprime (fully cosemiprime) comodules
Fully coprime (fully cosemiprime) corings
Fully coprime coradical
Fully coprime spectrum

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/s10485-006-9040-9

Cite this

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title = "Fully coprime comodules and fully coprime corings",

abstract = "Prime objects were defined as generalization of simple objects in the categories of rings (modules). In this paper we introduce and investigate what turns out to be a suitable generalization of simple corings (simple comodules), namely fully coprime corings (fully coprime comodules). Moreover, we consider several primeness notions in the category of comodules of a given coring and investigate their relations with the fully coprimeness and the simplicity of these comodules. These notions are applied then to study primeness and coprimeness properties of a given coring, considered as an object in its category of right (left) comodules.",

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author = "Abuhlail, \{Jawad Y.\}",

note = "Funding Information: Supported by King Fahd University of Petroleum and Minerals, Research Project \# INT/296. Funding Information: Acknowledgements Many thanks for the referee for the careful reading of the paper and for his/her suggestions, which improved the paper. The author thanks also Prof Stefaan Caenepeel for inviting him to submit a paper to this special issue of the journal. The author is grateful to Prof Robert Wisbauer and to Christian Lomp for fruitful discussions on the subject. He thanks also Virginia Rodrigues for sending him preprints of [9]. The author is also grateful for the financial support and the excellent research facilities provided by KFUPM.",

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doi = "10.1007/s10485-006-9040-9",

language = "English",

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N1 - Funding Information: Supported by King Fahd University of Petroleum and Minerals, Research Project # INT/296. Funding Information: Acknowledgements Many thanks for the referee for the careful reading of the paper and for his/her suggestions, which improved the paper. The author thanks also Prof Stefaan Caenepeel for inviting him to submit a paper to this special issue of the journal. The author is grateful to Prof Robert Wisbauer and to Christian Lomp for fruitful discussions on the subject. He thanks also Virginia Rodrigues for sending him preprints of [9]. The author is also grateful for the financial support and the excellent research facilities provided by KFUPM.

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N2 - Prime objects were defined as generalization of simple objects in the categories of rings (modules). In this paper we introduce and investigate what turns out to be a suitable generalization of simple corings (simple comodules), namely fully coprime corings (fully coprime comodules). Moreover, we consider several primeness notions in the category of comodules of a given coring and investigate their relations with the fully coprimeness and the simplicity of these comodules. These notions are applied then to study primeness and coprimeness properties of a given coring, considered as an object in its category of right (left) comodules.

AB - Prime objects were defined as generalization of simple objects in the categories of rings (modules). In this paper we introduce and investigate what turns out to be a suitable generalization of simple corings (simple comodules), namely fully coprime corings (fully coprime comodules). Moreover, we consider several primeness notions in the category of comodules of a given coring and investigate their relations with the fully coprimeness and the simplicity of these comodules. These notions are applied then to study primeness and coprimeness properties of a given coring, considered as an object in its category of right (left) comodules.

KW - Fully coprime (fully cosemiprime) comodules

KW - Fully coprime (fully cosemiprime) corings

KW - Fully coprime coradical

KW - Fully coprime spectrum

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VL - 14

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JO - Applied Categorical Structures

JF - Applied Categorical Structures

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ER -

Fully coprime comodules and fully coprime corings

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this