Algebraic structures sometimes need to be typed. For example, matrices over a ring form a ring, but the product is a only a partial operation: dimensions have to agree. Therefore, an easy way to look at matrices algebraically is to consider “typed rings”. We prove some “untyping” theorems: in some algebras (semirings, Kleene algebras, residuated monoids), types can be reconstructed from valid u...

The partial functions under disjoint-domain sums and functional composition do not form a field, and thus conventional linear algebra is not applicable. However they can be regarded as a so-ring, an algebraic structure possessing a natural partial ordering, an infinitary partial addition and a binary multiplication, subject to a set of axioms. In this paper, we introduce the notions of 2-absorb...

For a topological space X, and a topological ring A, let C(X,A) be the ring of all continuous functions from X into A under the pointwise multiplication. We show that the theorem "there is a completely regular space Y associated with a given topological space X such that C(Y,R) is isomorphic to C(X,R)" may be extended to a fairly large class of topologlcal rings, and that, in the study of algeb...

Let R be a commutative ring, V a nitely generated free R-module and G leGL R (V) a nite group acting naturally on the graded symmetric algebra A = S(V). Let (V; G) denote the minimal number m, such that the ring A G of inva riants can be generated by nitely many elements of degree at most m. For G = n and V (n; k), the k-fold direct sum of the natural permutat ion module, one knows that (V (n; ...

We use Grayson’s binary multicomplex presentation of algebraic K-theory to give a new construction of exterior power operations on the higher K-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a λ-ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial f...

In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous k-algebras A in terms of the dimension d, the codimension c, the initial degree q, and the length of the local cohomology modules of A. Next, we introduce the notion of Buchsbaum k-algebras with minimal multiplicity of degree q, and give several characterizations for those rings. In particular, we will show th...

In Section 2, after giving the basic definitions and some elementary consequences, we introduce two fundamental algebraic structures associated with a coherent configuration, namely, the boolean algebra of admissable relations and the adjacency ring. The action of a group on a finite set induces the structure of a coherent configuration in the set, and in this situations, which we refer to as t...

In this paper we analyse the homotopy type at primes p > 3 of the ring spectrum E`` representing a version of elliptic cohomology whose coefficient ring E``∗ agrees with the ring of modular forms for SL2(Z). For any prime (=maximal) graded ideal P / E``∗ containing the Eisenstein function Ep−1 as well as p, we show that there is a morphism of ring spectra [ E(2) −→ E`` b P and a corresponding s...

Effect algebras are the main object of study in quantum mechanics. Module measures those defined on an effect algebra with values a topological module. Let R be ring and M R-module. L algebra. The range module measure ?:L?M is studied. Among other results, we prove that if sRDP ?-effect natural basis ?:L?R countably additive measure, then ? has bounded variation.

The problem of imbedding an abstract distributive lattice in a Boolean algebra by an algebraic extension was suggested to the writer by M. H. Stone in 1933. Hausdorfff had already given a solution of this problem for the case where the given distributive lattice was a ring of point sets. A solution for the abstract case was presented by the writer to the Harvard Mathematical Colloquium (1934), ...