We reformulate the integrality property of the Poincaré inner product in the middle dimension, for an arbitrary Poincaré Q-algebra, in classical terms (discriminant and local invariants). When the algebra is 1-connected, we show that this property is the only obstruction to realizing it by a closed manifold, up to dimension 11. We reinterpret a result of Eisenbud and Levine on finite map germs,...

In this paper we study certain families of right ideals in noncommutative rings, called right Oka families, generalizing previous work on commutative rings by T.Y. Lam and the author. As in the commutative case, we prove that the right Oka families in a ring R correspond bijectively to the classes of cyclic right R-modules that are closed under extensions. We define completely prime right ideal...

We use the theory of resolutions for a given Hilbert function to investigate the multiplicity conjectures of Huneke and Srinivasan and Herzog and Srinivasan. To prove the conjectures for all modules with a particular Hilbert function, we show that it is enough to prove the statements only for elements at the bottom of the partially ordered set of resolutions with that Hilbert function. This ena...

In p-adic Hodge theory there are fully faithful functors from certain categories of p-adic representations of the Galois group GK := Gal(K/K) of a p-adic field K to certain categories of semi-linear algebra structures on finite-dimensional vector spaces in characteristic 0. For example, semistable representations give rise to weakly admissible filtered (φ,N)-modules, and Fontaine conjectured th...

Let (R,m) be a local ring (commutative and Noetherian). If R is complete (or, more generally, Henselian), one has the Krull-Schmidt uniqueness theorem for direct sums of indecomposable finitely generated R-modules. By passing to the m-adic completion b R, we can get a measure of how badly the Krull-Schmidt theorem can fail for a more general local ring. We assign to each finitely generated R-mo...

*Correspondence: [email protected] 2Otto-von-Guericke Universität, Magdeburg, Germany Full list of author information is available at the end of the article Abstract We describe an algorithm which finds binomials in a given ideal I ⊂ Q[x1, . . . , xn] and in particular decides whether binomials exist in I at all. Binomials in polynomial ideals can be well hidden. For example, the lowest degr...

1. Basics 2 1.1. Commutants 2 1.2. Opposite Rings 3 1.3. Units 3 1.4. Ideals 4 1.5. Modules 4 1.6. Division rings 5 1.7. Endomorphism rings 7 1.8. Monoid Rings 8 1.9. Noetherian and Artinian Rings 11 1.10. Simple rings 15 1.11. Prime ideals and prime rings 17 1.12. Notes 18 2. Wedderburn-Artin Theory 18 2.1. Semisimple modules and rings 18 2.2. Wedderburn-Artin I: Semisimplicity of Mn(D) 20 2.3...

the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...