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| In [[mathematics]], and more specifically in [[abstract algebra]], a '''pseudo-ring''' is one of the following variants of a [[ring (mathematics)|ring]]:
| | Oscar is how he's known as and he totally enjoys this title. Managing people is his occupation. North Dakota is her birth location but she will have to move one day or an additional. What I adore performing is taking part in baseball but I haven't made a dime with it.<br><br>My blog post :: [http://www.animecontent.com/user/D2456 home std test] |
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| * A [[rng (algebra)|rng]], i.e., a structure satisfying all the axioms of a ring except for the existence of a [[multiplicative identity]].<ref>{{Cite book
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| | last1=Bourbaki
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| | first1=N.
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| | author1-link=Nicolas Bourbaki
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| | title=Algebra I, Chapters 1-3
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| | publisher=Springer
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| | year=1998
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| | page=98
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| }}</ref>
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| * A set ''R'' with two [[binary operation]]s + and · such that (''R'',+) is an [[abelian group]] with [[additive identity|identity]] 0, and <math>a(b+c) + a0 =ab +ac</math> and <math>(b+c)a +0a=ba+ca</math> for all ''a'', ''b'', ''c'' in ''R''.<ref name=Natarajan>{{cite journal|last=Natarajan|first=N. S.|title=Rings with generalised distributive laws|journal=J. Indian. Math. Soc. (N. S.)|year=1964|volume=28|pages=1-6}}</ref>
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| * An abelian group (''A'',+) equipped with a [[subgroup]] ''B'' and a multiplication ''B'' × ''A'' → ''A'' making ''B'' a ring and ''A'' a ''B''-[[module (mathematics)|module]].<ref name=Patterson>{{cite journal|last=Patterson|first=Edward M.|title=The Jacobson radical of a pseudo-ring|journal=Math. Z.|year=1965|volume=89|pages=348-364}}</ref>
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| No two of these definitions are equivalent, so it is best to avoid the term "pseudo-ring" or to clarify which meaning is intended.
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| == References ==
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| {{reflist}}
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| {{DEFAULTSORT:Pseudo-ring}}
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| [[Category:Ring theory]]
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| [[Category:Algebraic structures]] | |
| [[Category:Algebras]]
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Latest revision as of 15:22, 16 April 2014
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