Non-Free Projective Modules for Torsion-Free Groups In [2] it was shown that the trefoil group T= gp (a, b a2—b3) has a module which is projective but not free. In this paper, using similar methods, we construct some more examples of non-free projective modules for torsion-free grou...
Quillen's solution of Serre's problem is extended to Laurent polynomial rings. An example is given of a A[ T, T-1 ]-module P which is not extended even tho... Swan,G Richard - 《Transactions of the American Mathematical Society》 被引量: 255发表: 1978年 Finitely generated projective ...
On the other hand, we exhibit a 6-dimensional algebra 3 with a semi-Gorenstein-projective module M which is not torsionless (thus not Gorenstein-projective). Actually, also the 3-dual module M* is semi-Gorenstein-projective. In this way, we show the independence of the total reflexivity ...
ANDERSON'S CONJECTURE AND THE MAXIMAL MONOID CLASS OVER WHICH PROJECTIVE MODULES ARE FREE A positive solution is given to a conjecture of D. F. Anderson (Pacific J. Math. 79(1978), 5-17, p. 11) concerning freeness of finitely generated projective modules over normal monoid algebras. In ...
a module need not always have one. Modules possessing a basis are called free. So a finitely generated free R-module is of the form Rn for some n E IN, equipped with the usual operations. A module is called p- jective, iff it is a direct summand of a free one. Especially a finit...
Finally, we prove that a ring R is relative left hereditary if and only if every submodule of a projective (or free) left R-module is n-copure projective if and only if id R (N)≤ 1 for every left R-module N with N∈ F n ....
) is not a direct summand of a free R -semimodule. 3. Characterizations of projective and k-projective semimodules. We character- ize projective and k-projective semimodules via the Hom functor. We state and prove the following lemma and corollaries which are needed in the proof of Theorem...
We want to present a notion of quantum principal bundle that is more general than that of Hopf–Galois extension presented in Definition 2.3, and which can accomodate also the case where M is an algebraic variety, which is not affine. To this end, we consider a sheaf theoretic description ...
Projective simulation is based on a random walk through a network of clips, which are elementary patches of episodic memory. The network of clips changes dynamically, both due to new perceptual input and due to certain compositional principles of the simulation process. During simulation, the clips...
In addition, equations (1.82) imply that the parallel displacements form a subgroup which is not an invariant subgroup. A Euclidean space En is obtained from an affine space An if in the ideal hyperplane of the latter space a nondegenerate imaginary quadric Q of dimension n − 2 is fixed...