The special circulant matrix and units in group rings.
The spectral radius of the Coxeter transformations for a generalized Cartan matrix.
The spectral topology in rings
The spectral topology of a ring is easily defined, has familiar applications in elementary Banach algebra theory, and appears relevant to abstract Fredholm and stable range theory.
The spectrum of a Cartesian product of plural algebras
The standard form of a representation-finite algebra
The Strong Anick Conjecture is true
Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra over a field of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of . In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a...
The structure of Loewy modules.
The structure of Morita dual monoids.
The structure of primary modules
The Structure of *-simple Involution Rings with Minimal *-Biideals
The structure of the unit group of the group algebra
The structure of the unit group of the group algebra of the group over any finite field of characteristic 2 is established in terms of split extensions of cyclic groups.
The structures of Hopf -algebra on Radford algebras
We investigate the structures of Hopf -algebra on the Radford algebras over . All the -structures on are explicitly given. Moreover, these Hopf -algebra structures are classified up to equivalence.
The Sub-Semi-Groups Excluding Zero of a Near-Ring.
The symmetry of unit ideal stable range conditions
In this paper, we prove that unit ideal-stable range condition is right and left symmetric.
The symplectic Gram-Schmidt theorem and fundamental geometries for -modules
Like the classical Gram-Schmidt theorem for symplectic vector spaces, the sheaf-theoretic version (in which the coefficient algebra sheaf is appropriately chosen) shows that symplectic -morphisms on free -modules of finite rank, defined on a topological space , induce canonical bases (Theorem 1.1), called symplectic bases. Moreover (Theorem 2.1), if is an -module (with respect to a -algebra sheaf without zero divisors) equipped with an orthosymmetric -morphism, we show, like in the classical...
The tropical Grassmannian.
The unit group of .
The universal skew field of fractions ofa tensor product of free rings
The upper central series of some matrix groups
The vanishing of self-extensions over n-symmetric algebras of quasitilted type
A ring Λ satisfies the Generalized Auslander-Reiten Condition ( ) if for each Λ-module M with for all i > n the projective dimension of M is at most n. We prove that this condition is satisfied by all n-symmetric algebras of quasitilted type.