We compute the total Witt groups of (split) Grassmann varieties, over any regular base X. The answer is a free module over the total Witt ring of X. We provide an explicit basis for this free module, which is indexed by a special class of Young diagrams, that we call even Young diagrams.

The Montgomery inversion is a fundamental computation in several cryptographic applications. In this work, we propose a scalable hardware architecture to compute the Montgomery modular inverse in GF(p). We suggest a new correction phase for a previously proposed almost Montgomery inverse algorithm to calculate the inversion in hardware. The intended architecture is scalable, which means that a ...

The purpose of this paper is to study the cyclic self orthogonal codes over Zpm . After providing the generator polynomial of cyclic self orthogonal codes over Zpm , we give the necessary and sufficient condition for the existence of non-trivial self orthogonal codes over Zpm . We have also provided the number of such codes of length n over Zpm for any (p, n) = 1.

Indecomposable Schur rings over a cyclic group Zn of order n are considered. In the case n = p, p an odd prime, the total number of such rings was described in terms of Catalan numbers by Liskovets and Pöschel [Discr. Math. 214 (2000), 173–191]. Here, a closed formula is shown for the total number of indecomposable Schur rings over Z2m using Catalan and Schröder numbers. The result is obtained ...

The purpose of this note is to point out an interesting connection between the structure of a commutative, Noetherian ring of prime characteristic as a (left) module over its ring of diierential operators and various well studied properties such as F-purity, F-regularity, and strong F-regularity. Theorem 2.2 establishes the rst connections between the D-module structure of rings of characterist...

In our work [9], we complete Jans’ classification of TTF-triples [8] by giving a precise description of those two-sided ideals of a ring associated to one-sided split TTF-triples in the corresponding module category.

Let (S,≤) be a strictly totally ordered monoid, R be a commutative ring and M be an R-module. We show the following results: (1) If (S,≤) satisfies the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a semi Hopfian [[RS,≤]]-module if and only if M is a semi Hopfian R-module; (2) If (S,≤) is artinian, then the generalized inverse polynomial module [MS,...

Given a ring homomorphism B → A, consider its centralizer R = A, bimodule endomorphism ring S = EndBAB and sub-tensor-square ring T = (A ⊗B A) B . Nonassociative tensoring by the cyclic modules RT or SR leads to an equivalence of categories inverse to the functors of induction of restricted A-modules or restricted coinduction of B-modules in case A |B is separable, H-separable, split or left de...