東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Intrinsic and Dense Intrinsic Extens...

Lennon, Matthew J., IV.

FindBook

Google Book

Amazon

博客來

Intrinsic and Dense Intrinsic Extensions of Rings.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Intrinsic and Dense Intrinsic Extensions of Rings./
作者:	Lennon, Matthew J., IV.
面頁冊數:	85 p.
附註:	Source: Dissertation Abstracts International, Volume: 74-12(E), Section: B.
Contained By:	Dissertation Abstracts International74-12B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3590017
ISBN:	9781303292224

Intrinsic and Dense Intrinsic Extensions of Rings.
Lennon, Matthew J., IV.

Intrinsic and Dense Intrinsic Extensions of Rings. - 85 p.

Source: Dissertation Abstracts International, Volume: 74-12(E), Section: B.

Thesis (Ph.D.)--University of Louisiana at Lafayette, 2013.

In 1964, Carl Faith and Yuzo Utumi introduced the notion of an intrinsic extension of a ring. In this dissertation, the notion is generalized and studied in its own right. Suppose R is a subring of T. The ring, T, is said to be a right intrinsic extension of R if every nonzero right ideal of T has nonzero intersection with R. This concept is a natural generalization of an essential extension of a ring. We define an analogous generalization of a dense extension of a ring called a dense intrinsic extension. If R is a subring of T, we say T is a dense intrinsic extension of R if for each t1, t2 in T with t1 not 0, there exists s in T such that 0 is not equal to t 1s and t2s in R. In this dissertation we show that several important ring properties are able to be transferred across these types of extensions. In particular, the extending, quasi-continuous, G -extending, FI-extending, and Kasch properties are examined amongst others. It is also shown that with mild conditions on the base ring, a complete set of primitive (respectively, centrally primitive idempotents, left triangulating idempotents) can be constructed for a (dense) intrinsic extension, T, from a corresponding set in the base ring, R. Examples and applications are given for rings that occur in functional analysis and group ring theory.

ISBN: 9781303292224Subjects--Topical Terms:

515831
Mathematics.

Intrinsic and Dense Intrinsic Extensions of Rings.
LDR:02185nam a2200277 4500 001 1967888
005 20141121132938.5
008 150210s2013 ||||||||||||||||| ||eng d
020 $a 9781303292224
035 $a (MiAaPQ)AAI3590017
035 $a AAI3590017
040 $a MiAaPQ $c MiAaPQ
100 1 $a Lennon, Matthew J., IV. $3 2104978
245 1 0 $a Intrinsic and Dense Intrinsic Extensions of Rings.
300 $a 85 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-12(E), Section: B.
500 $a Adviser: Gary F. Birkenmeier.
502 $a Thesis (Ph.D.)--University of Louisiana at Lafayette, 2013.
520 $a In 1964, Carl Faith and Yuzo Utumi introduced the notion of an intrinsic extension of a ring. In this dissertation, the notion is generalized and studied in its own right. Suppose R is a subring of T. The ring, T, is said to be a right intrinsic extension of R if every nonzero right ideal of T has nonzero intersection with R. This concept is a natural generalization of an essential extension of a ring. We define an analogous generalization of a dense extension of a ring called a dense intrinsic extension. If R is a subring of T, we say T is a dense intrinsic extension of R if for each t1, t2 in T with t1 not 0, there exists s in T such that 0 is not equal to t 1s and t2s in R. In this dissertation we show that several important ring properties are able to be transferred across these types of extensions. In particular, the extending, quasi-continuous, G -extending, FI-extending, and Kasch properties are examined amongst others. It is also shown that with mild conditions on the base ring, a complete set of primitive (respectively, centrally primitive idempotents, left triangulating idempotents) can be constructed for a (dense) intrinsic extension, T, from a corresponding set in the base ring, R. Examples and applications are given for rings that occur in functional analysis and group ring theory.
590 $a School code: 1363.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical Mathematics. $3 1672766
690 $a 0405
690 $a 0642
710 2 $a University of Louisiana at Lafayette. $b Mathematics. $3 2104979
773 0 $t Dissertation Abstracts International $g 74-12B(E).
790 $a 1363
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3590017