Varieties and radicals of near-rings

Stefan Veldsman

doi:10.1007/BF03322344

Varieties and radicals of near-rings

Stefan Veldsman^*

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

It is shown that a variety of associative rings which has attainable identities in the class of all associatives ring has attainable identities in the class of all near—rings. We also give examples of varieties of near-rings which are, contrary to the ring case, closed under extensions but do not have attainable identities and varieties which are closed under extensions but not closed under essential extensions, respectively.

Original language	English
Pages (from-to)	356-371
Number of pages	16
Journal	Results in Mathematics
Volume	24
Issue number	3
DOIs	https://doi.org/10.1007/BF03322344
Publication status	Published - Nov 1993
Externally published	Yes

Keywords

16Y30
attainable identities
radical class
semisimple class
variety

ASJC Scopus subject areas

Mathematics (miscellaneous)
Applied Mathematics

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10.1007/BF03322344

Cite this

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title = "Varieties and radicals of near-rings",

abstract = "It is shown that a variety of associative rings which has attainable identities in the class of all associatives ring has attainable identities in the class of all near—rings. We also give examples of varieties of near-rings which are, contrary to the ring case, closed under extensions but do not have attainable identities and varieties which are closed under extensions but not closed under essential extensions, respectively.",

keywords = "16Y30, attainable identities, radical class, semisimple class, variety",

author = "Stefan Veldsman",

year = "1993",

month = nov,

doi = "10.1007/BF03322344",

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volume = "24",

pages = "356--371",

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AU - Veldsman, Stefan

PY - 1993/11

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N2 - It is shown that a variety of associative rings which has attainable identities in the class of all associatives ring has attainable identities in the class of all near—rings. We also give examples of varieties of near-rings which are, contrary to the ring case, closed under extensions but do not have attainable identities and varieties which are closed under extensions but not closed under essential extensions, respectively.

AB - It is shown that a variety of associative rings which has attainable identities in the class of all associatives ring has attainable identities in the class of all near—rings. We also give examples of varieties of near-rings which are, contrary to the ring case, closed under extensions but do not have attainable identities and varieties which are closed under extensions but not closed under essential extensions, respectively.

KW - 16Y30

KW - attainable identities

KW - radical class

KW - semisimple class

KW - variety

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U2 - 10.1007/BF03322344

DO - 10.1007/BF03322344

M3 - Article

AN - SCOPUS:84888610784

SN - 0378-6218

VL - 24

SP - 356

EP - 371

JO - Results in Mathematics

JF - Results in Mathematics

IS - 3

ER -

Varieties and radicals of near-rings

Abstract

Keywords

ASJC Scopus subject areas

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