Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 신경희 | - |
dc.creator | 신경희 | - |
dc.date.accessioned | 2016-08-26T02:08:48Z | - |
dc.date.available | 2016-08-26T02:08:48Z | - |
dc.date.issued | 1994 | - |
dc.identifier.other | OAK-000000000735 | - |
dc.identifier.uri | https://dspace.ewha.ac.kr/handle/2015.oak/192100 | - |
dc.identifier.uri | http://dcollection.ewha.ac.kr/jsp/common/DcLoOrgPer.jsp?sItemId=000000000735 | - |
dc.description.abstract | This dissertation studies the Schur group of a Krull domain. Let R be a Krull domain with the field of fractions K and S(R) be the Schur subgroup of the Brauer group B(R) over R. We define the Schur group of a refiexive R-module category over a Krull domain R. And thus, we obtain the exact sequence between the class group and the Schur group of reflexive module categories over R. If R[x] is the polynomial ring of a Krull domain R then we show that the quotient group SCl(R[x])/SCl(R) coincides with the kernel of S(R[x]) → S(R). Let I be an ideal in the radical of a commutative ring R. If R is complete in its I-adic topology then we obtain that S(R) ~ S(R/I). ; 환 R이 Krull domain일 때 reflexive R-module 카테고리(category)상에서의 Schur군을 정의하고 같은 카테고리 상에서 class군과 Schur군을 포함하는 exact sequence가 존재함을 보인다. R[x]가 환 R에서의 다항식 환 일 대 상군 SCl(R[x])/SCl(R)과 S(R[x]) → S(R)의 핵은 같다. 또한 환 R이complete이고 I가 환 R의 ideal일 때 환 R의 Schur군과 법 I에서의 환 R의 Schur군은 같음을 보인다. | - |
dc.description.tableofcontents | Introduction --------------------------------------------------------- 1 I. Reflexive modules over Krull domain ------------------------------- 5 II. The Schur group for module categories ---------------------------- 11 III. Functoriality --------------------------------------------------- 20 IV. The Schur group of polynomial rings over Krull domain ------------ 24 V. The Schur group of a ring modulo an ideal ------------------------- 28 References ----------------------------------------------------------- 31 Korean abstract ------------------------------------------------------ 34 | - |
dc.format | application/pdf | - |
dc.format.extent | 1041533 bytes | - |
dc.language | eng | - |
dc.publisher | 이화여자대학교 대학원 | - |
dc.title | The Schur group of a Krull domain | - |
dc.type | Doctoral Thesis | - |
dc.identifier.thesisdegree | Doctor | - |
dc.identifier.major | 대학원 수학과 | - |
dc.date.awarded | 1994. 2 | - |