L-Theory and the Arf Invariant.
Lusztig conjectures, old and new, I.
L-zero-divisor graphs of direct products of L-commutative rings
L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-ziro-divisor graph of a L-ring when extending to a finite direct product of L-commutative rings.
-density, -adic completion and -subgeneration
- системы и - компоненты идеалов
MacLane homology and topological Hochschild homology.
Mal'tsev--Neumann products of semi-simple classes of rings
Malt’tsev–Neumann products of semi-simple classes of associative rings are studied and some conditions which ensure that such a product is again a semi-simple class are obtained. It is shown that both products, and of semi-simple classes and are semi-simple classes if and only if they are equal.
Maps of cotriples and a change of rings theorem
Maps on upper triangular matrices preserving zero products
Consider —the ring of all upper triangular matrices defined over some field . A map is called a zero product preserver on in both directions if for all the condition is satisfied if and only if . In the present paper such maps are investigated. The full description of bijective zero product preservers is given. Namely, on the set of the matrices that are invertible, the map may act in any bijective way, whereas for the zero divisors and zero matrix one can write as a composition...
Matching local Witt invariants
The starting point of this note is the observation that the local condition used in the notion of a Hilbert-symbol equivalence and a quaternion-symbol equivalence — once it is expressed in terms of the Witt invariant — admits a natural generalisation. In this paper we show that for global function fields as well as the formally real function fields over a real closed field all the resulting equivalences coincide.
Matrices carrées sur l'algèbre de Weyl
Matrices of positive polynomials.
Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras
Let Λ be a directed finite-dimensional algebra over a field k, and let B be an upper triangular bimodule over Λ. Then we show that the category of B-matrices mat B admits a projective generator P whose endomorphism algebra End P is quasi-hereditary. If A denotes the opposite algebra of End P, then the functor Hom(P,-) induces an equivalence between mat B and the category ℱ(Δ) of Δ-filtered A-modules. Moreover, any quasi-hereditary algebra whose category of Δ-filtered modules is equivalent to mat...
Matrix divisibility sequences
Matrix factorizations for domestic triangle singularities
Working over an algebraically closed field k of any characteristic, we determine the matrix factorizations for the-suitably graded-triangle singularities of domestic type, that is, we assume that (a,b,c) are integers at least two satisfying 1/a + 1/b + 1/c > 1. Using work by Kussin-Lenzing-Meltzer, this is achieved by determining projective covers in the Frobenius category of vector bundles on the weighted projective line of weight type (a,b,c). Equivalently, in a representation-theoretic context,...
Matrix identities involving multiplication and transposition
We study matrix identities involving multiplication and unary operations such as transposition or Moore–Penrose inversion. We prove that in many cases such identities admit no finite basis.
Matrix problems and Drozd's theorem
Matrix problems and stable homotopy types of polyhedra
This is a survey of the results on stable homotopy types of polyhedra of small dimensions, mainly obtained by H.-J. Baues and the author [3, 5, 6]. The proofs are based on the technique of matrix problems (bimodule categories).
Matrix rings with summand intersection property
A ring has right SIP (SSP) if the intersection (sum) of two direct summands of is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property. We also prove that the trivial extension of by has SIP if and only if has SIP and for every idempotent in . Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP.
Matrix versions of aperiodic -rational identities