Fundamental Notions in Ring Theory

2002 ◽  
pp. 1-27
Author(s):  
Gilberto Bini ◽  
Flaminio Flamini
Keyword(s):  
Ring Theory

FPF Ring Theory

1984 ◽  
Author(s):  
Carl Faith ◽  
Stanley Page
Keyword(s):  
Ring Theory

A Conceptual Study on Differences in National R&D Activities Using O-ring Theory Approach

2013 ◽  
Vol 27 (4) ◽  
pp. 521-534
Author(s):  
Chi-Ung Song ◽  
Young Jun Kim
Keyword(s):  
Ring Theory ◽  
Theory Approach ◽  
Conceptual Study

scholarly journals Hybridization of ring theory-based evolutionary algorithm and particle swarm optimization to solve class imbalance problem

2021 ◽  
Author(s):  
Sayan Surya Shaw ◽  
Shameem Ahmed ◽  
Samir Malakar ◽  
Laura Garcia-Hernandez ◽  
Ajith Abraham ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Real Life ◽  
Class Imbalance ◽  
Ring Theory ◽  
Class Imbalance Problem ◽  
Minority Class ◽  
Swarm Optimization ◽  
Imbalance Problem ◽  
Representative Samples ◽  
Selection Of

AbstractMany real-life datasets are imbalanced in nature, which implies that the number of samples present in one class (minority class) is exceptionally less compared to the number of samples found in the other class (majority class). Hence, if we directly fit these datasets to a standard classifier for training, then it often overlooks the minority class samples while estimating class separating hyperplane(s) and as a result of that it missclassifies the minority class samples. To solve this problem, over the years, many researchers have followed different approaches. However the selection of the true representative samples from the majority class is still considered as an open research problem. A better solution for this problem would be helpful in many applications like fraud detection, disease prediction and text classification. Also, the recent studies show that it needs not only analyzing disproportion between classes, but also other difficulties rooted in the nature of different data and thereby it needs more flexible, self-adaptable, computationally efficient and real-time method for selection of majority class samples without loosing much of important data from it. Keeping this fact in mind, we have proposed a hybrid model constituting Particle Swarm Optimization (PSO), a popular swarm intelligence-based meta-heuristic algorithm, and Ring Theory (RT)-based Evolutionary Algorithm (RTEA), a recently proposed physics-based meta-heuristic algorithm. We have named the algorithm as RT-based PSO or in short RTPSO. RTPSO can select the most representative samples from the majority class as it takes advantage of the efficient exploration and the exploitation phases of its parent algorithms for strengthening the search process. We have used AdaBoost classifier to observe the final classification results of our model. The effectiveness of our proposed method has been evaluated on 15 standard real-life datasets having low to extreme imbalance ratio. The performance of the RTPSO has been compared with PSO, RTEA and other standard undersampling methods. The obtained results demonstrate the superiority of RTPSO over state-of-the-art class imbalance problem-solvers considered here for comparison. The source code of this work is available in https://github.com/Sayansurya/RTPSO_Class_imbalance.

scholarly journals On matrix methods in ring theory

1973 ◽  
Vol 8 (1) ◽  
pp. 159-160
Author(s):  
George Ivanov
Keyword(s):  
Ring Theory ◽  
Matrix Methods

scholarly journals Flatness and absolute purity applying functor categories to ring theory

1977 ◽  
Vol 44 (2) ◽  
pp. 411-419 ◽  
Author(s):  
Harro Bernecker
Keyword(s):  
Ring Theory ◽  
Functor Categories

scholarly journals On essential extensions of rings

1987 ◽  
Vol 35 (3) ◽  
pp. 379-386 ◽  
Author(s):  
E. R. Puczyłwski
Keyword(s):  
Ring Theory ◽  
Essential Ideal ◽  
Essential Extensions

This paper concerns the problem of description of the set of rings containing a given ring as an essential ideal. The results obtained are applied to some problems of ring theory and radicals.

Arithmetic of matrices over rings

2021 ◽  
Author(s):  
V.P. Shchedryk ◽  
Keyword(s):  
Graduate Students ◽  
Normal Form ◽  
Matrix Factorization ◽  
Ring Theory ◽  
Stable Range ◽  
Matrix Rings ◽  
Principal Ideals ◽  
Factorization Theory ◽  
Close Relationship ◽  
The Matrix

The book is devoted to investigation of arithmetic of the matrix rings over certain classes of commutative finitely generated principal ideals do- mains. We mainly concentrate on constructing of the matrix factorization theory. We reveal a close relationship between the matrix factorization and specific properties of subgroups of the complete linear group and the special normal form of matrices with respect to unilateral equivalence. The properties of matrices over rings of stable range 1.5 are thoroughly studied. The book is intended for experts in the ring theory and linear algebra, senior and post-graduate students.

Sign in / Sign up

Export Citation Format

Share Document