Universal gradings of orders

arXiv (Cornell University), 2022

Communications in Algebra, 2005

Journal of Mathematics, 2013

For any finite abelian group(R,+), we define a binary operation or “multiplication” onRand give necessary and sufficient conditions on this multiplication forRto extend to a ring. Then we show when two rings made on the same group are isomorphic. In particular, it is shown that there aren+1rings of orderpnwith characteristicpn, wherepis a prime number. Also, all finite rings of orderp6are described by generators and relations. Finally, we give an algorithm for the computation of all finite rings based on their additive group.

Osaka Journal of Mathematics - OSAKA J MATH, 1983

IOSR Journals , 2019

Several people presented solutions to the Birkhoff’s problem “Develop a common abstraction which includes Boolean algebras (rings) and lattice ordered groups as special cases”. Many common abstractions namely dually residuated lattice ordered semi groups, lattice ordered groups, DRℓ - groups, lattice ordered rings are presented in [6], [4], [3] and [2] respectively. The objective of this paper is to introduce Characterization Theorem for commutative lattice ordered ring or commutative ℓ-ring which is an abstraction between Boolean algebra and lattice ordered group.

We here deal with a multiparty algorithm, a system of rules about the correct way to act in formal situations. These are defined by a sequence of steps revealing the actions required of two or more parties so that a specified objective may be achieved. Here we discuss a shortened algebraic fundamental establishment of such an algorithm and would be followed by ring (near-ring) theoretical illustration for secrecy, in obvious sense between two parties, whose only means of communication is a mass channel.

Semigroup Forum, 2014

Journal of the London Mathematical Society, 1985