In this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of ZZn ⊕ T with no invertible elements, where T is a finite abelian group. We also characterize the lattice ideals that are set-theoretic complete intersections on binomials.

Given a probability measure on finitely generated group, its Martin boundary is way to compactify the group using Green's function of corresponding random walk. We give complete topological characterization supported walks relatively hyperbolic groups with virtually abelian parabolic subgroups. In particular, in case nonuniform lattices real space H n , we show that coincides CAT (0) truncated ...

A finitely generated group is called a Church-Rosser group (growing contextsensitive group) if it admits a finitely generated presentation for which the word problem is a Church-Rosser (growing context-sensitive) language. Although the ChurchRosser languages are incomparable to the context-free languages under set inclusion, they strictly contain the class of deterministic context-free language...

Let R be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented R-modules that are closed under extensions. We also classify abelian subcategories of arbitrary R-modules that are closed under extensions and coproducts, when R is commutative and Noetherian. The method relies on comparison with ...

We show that two C∗-algebraic noncommutative tori are strongly Morita equivalent if and only if they have isomorphic ordered K0-groups and centers, extending N. C. Phillips’s result in the case that the algebras are simple. This is also generalized to the twisted group C∗-algebras of arbitrary finitely generated abelian groups.

Staggered formalism of lattice fermion can be cast into a form of direct product K-cycle in noncommutative geometry. The correspondence between this staggered K-cycle and a canonically defined K-cycle for finitely generated abelian group where lattice appears as a special case is proved. PACS: 02.40.Gh, 11.15.Ha, 02.20.Bb

We show that for each genus there are only finitely many algebraically primitive Teichmüller curves C, such that i) C lies in the hyperelliptic locus and ii) C is generated by an abelian differential with two zeros of order g − 1. We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.

We show that every finitely generated non-abelian free group Γ admits a spherically transitive action on a rooted tree T such that the action of Γ on the boundary of T is not essentially free. This reproves a result of Bergeron and Gaboriau. The existence of such an action answers a question of Grigorchuk, Nekrashevich and Sushchanskii.

Let $p$ be a prime number, $k$ finite field of characteristic $p>0$ and $K/k$ finitely generated extension fields. $A$ $K$ -abelian variety such that all the isogeny factors are neither isotrivial nor -rank zero. We give necessary sufficient condition for generation $A(K^{\mathrm {perf}})$ in terms action $\mathrm {End}(A)\otimes \mathbb {Q}_p$ on -divisible group $A[p^{\infty }]$ . In parti...

We show that the semi-simplicity conjecture for finitely generated fields follows from conjunction of finite and maximal abelian extension field rational numbers.