Let kG denote the group ring of the group G over a commutative ring k. If M is a finitely generated projective kG-module, then the Hattori- Stallings trace yields a rank r M which is a class function on G. Specifically it is defined as follows. Let N be a kG-module such that M...
The projective dimension ofis. Thei-th Betti number ofis the rank of the free module, i.e.,; and the Betti sequence ofis. When the Krull dimension ofcoincides with its depth as-module, the ringis said to be Cohen-Macaulay. By the Auslander-Buchsbaum formula, this is equivalent to. Whe...
the case of threefolds. The first non-trivial bundles appear in rank two and we will particularly study this case. When the Picard number ϱ(F) is 1, a complete classification of indecomposable aCM bundles of rank 2 on F has been given by E. Arrondo and L. Costa (see [2]) using...
package{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C(S^{4}_{heta})}$$\end{document}is a sum of a rank-1 module and a free module. ...
RG Swan,J Towber - 《Journal of Algebra》 被引量: 92发表: 1975年 Monads on projective spaces Let be a vector bundle on P n . There is a strong relationship between and its intermediate cohomology modules. In the case where has low rank, we exploit ... NM Kumar,CPP Rao - 《Manuscrip...
Standard Hilbert C∗-module frames View PDFReferences [1] C. Badea The stable rank of topological algebras and a problem of R.G. Swan J. Funct. Anal., 160 (1) (1998), pp. 42-78 View PDFView articleView in ScopusGoogle Scholar [2] R. Balan, P.G. Casazza, C. Heil, Z. Land...
} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${C(S^{4}_{heta})}$$\\end{document}is a sum of a rank-1 module and a free module....
Our integral formulas are explicitly constructed out of a resolution (1.4). Recall that the (Castelnuovo–Mumford) regularity of X is defined as the regularity of the ideal JX which turns out to be 1 plus the regularity of the module S/JX, so that regX=maxk,i(dki−k)+1, if (1.4...
(1) Uniserial module U is quasi-projective if and only if it is weakly quasi-projective and an additional technical requirement is satisfied. (2) For torsion free modules of rank 1, quasi-projectivity is equivalent to the weak quasi-projectivity, and the latter is determined by completeness...
Projective $D\\lbrack x, y brack$-modules of rank $\\geqslant 2$ are free. Projective id... M.-A. Knus and M. Ojanguren - 《Proceedings of the American Mathematical Society》 被引量: 47发表: 1977年 On the rate of points in projective spaces The rate of a standard graded K -...