کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9493441 | 1334241 | 2005 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Dimension and torsion theories for a class of Baer *-rings
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Dimension and torsion theories for a class of Baer *-rings Dimension and torsion theories for a class of Baer *-rings](/preview/png/9493441.png)
چکیده انگلیسی
Many known results on finite von Neumann algebras are generalized, by purely algebraic proofs, to a certain class C of finite Baer *-rings. The results in this paper can also be viewed as a study of the properties of Baer *-rings in the class C. First, we show that a finitely generated module over a ring from the class C splits as a direct sum of a finitely generated projective module and a certain torsion module. Then, we define the dimension of any module over a ring from C and prove that this dimension has all the nice properties of the dimension studied in [W. Lück, J. Reine Angew. Math. 495 (1998) 135-162] for finite von Neumann algebras. This dimension defines a torsion theory that we prove to be equal to the Goldie and Lambek torsion theories. Moreover, every finitely generated module splits in this torsion theory. If R is a ring in C, we can embed it in a canonical way into a regular ring Q also in C. We show that K0(R) is isomorphic to K0(Q) by producing an explicit isomorphism and its inverse of monoids Proj(P)âProj(Q) that extends to the isomorphism of K0(R) and K0(Q).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 289, Issue 2, 15 July 2005, Pages 614-639
Journal: Journal of Algebra - Volume 289, Issue 2, 15 July 2005, Pages 614-639
نویسندگان
Lia Vaš,