Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with coefficients in R. In the case when the ring R is a field, every pair is equivalent to a homogeneous system. Using the formal matrix calculus, two alternate pr...

In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...

For a module-finite algebra over commutative noetherian ring, we give complete description of flat cotorsion modules in terms prime ideals the algebra, as generalization Enochs' result for ring. As consequence, show that pointwise Matlis duality gives bijective correspondence between isoclasses indecomposable injective left and right modules. This is an explicit realization Herzog's homeomorphi...

In this paper we describe the defining equations of the Rees algebra and the special fiber ring of a truncation I of a complete intersection ideal in a polynomial ring over a field with homogeneous maximal ideal m. To describe explicitly the Rees algebra R(I) in terms of generators and relations we map another Rees ring R(M) onto it, where M is the direct sum of powers of m. We compute a Gröbne...

It is proved that for a ring R either an affine algebra over field, or equicharacteristic complete local ring, some power of the Jacobian ideal annihilates ExtRd+1(−,−), where d Krull dimension R. Sufficient conditions are identified under which itself these Ext-modules, and examples provided show this not always case. The crucial new idea to consider derived version Noether different algebra.

A result of Artin, Small, and Zhang is used to show that a noetherian algebra over a commutative, noetherian Jacobson ring will be Jacobson if the algebra possesses a locally finite, noetherian associated graded ring. This result is extended to show that if an algebra over a commutative noetherian ring has a locally finite, noetherian associated graded ring, then the intersection of the powers ...

Classical obstruction theory can be applied to the problem of finding an S-algebra structure, or a commutative S-algebra structure, on a ring spectrum. It is shown that there is no obstruction to upgrading the homotopy unit in the ring spectrum to a strict unit in the S-algebra.

We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism f from a Banach algebra into a semisimple commutative...

Theorem: An AW*-algebra is the ring generated by its projections if and only if it has no abelian summand. Corollary: Every equivalence in an A W*-algebra may be implemented by a partial isometry in the ring generated by the projections of the algebra. The corollary is extended to certain finite Baer »-rings. An early proposition in the theory of von Neumann algebras is that every such algebra ...

the aim of this paper is to study orders over a valuation ring v with arbitrary rank in acentral simple f-algebra q. the relation between all of the orders is explained with a diagram. it is thenshown that inside bezout order, extremal v-orders are precisely semi-hereditary. in the last section, theeffect of henselization on maximal and semi-hereditary orders is examined.