國立虎尾科技大學 |

Free ideal rings and localization in general rings /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Free ideal rings and localization in general rings // P.M. Cohn.
其他題名:	Free Ideal Rings & Localization in General Rings
作者:	Cohn, P. M.
面頁冊數:	1 online resource (xxii, 572 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Associative algebras. -
電子資源:	https://doi.org/10.1017/CBO9780511542794
ISBN:	9780511542794 (ebook)

Free ideal rings and localization in general rings /
Cohn, P. M.

Free ideal rings and localization in general rings /Free Ideal Rings & Localization in General RingsP.M. Cohn. - 1 online resource (xxii, 572 pages) :digital, PDF file(s). - New mathematical monographs ;3. - New mathematical monographs ;31..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Generalities on rings and modules --1.

Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note.

ISBN: 9780511542794 (ebook)Subjects--Topical Terms:

686514
Associative algebras.

LC Class. No.: QA247 / .C636 2006

Dewey Class. No.: 512.4

Free ideal rings and localization in general rings /
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505 0 0 $t Generalities on rings and modules -- $g 1. $t Principal ideal domains -- $g 2. $t Firs, semifirs and the weak algorithm -- $g 3. $t Factorization in semifirs -- $g 4. $t Rings with a distributive factor lattice -- $g 5. $t Modules over firs and semifirs -- $g 6. $t Centralizers and subalgebras -- $g 7. $t Skew fields of fractions.
520 $a Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note.
650 0 $a Associative algebras. $3 686514
650 0 $a Ideals (Algebra) $3 678238
650 0 $a Rings (Algebra) $3 786669
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