Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
NJ-Abelian Rings: an Abelian-Like Approach
View through CrossRef
This article extends the concept of NJ-semicommutative rings to introduce the broader class of NJ-abelian rings, which are defined by properties involving nilpotent elements and the Jacobson radical. We investigate the unique algebraic properties of NJ-abelian rings and analyze their relationships with various types of rings, including abelian, reduced, J-clean, local, and Dedekind-finite rings. In particular, we show that every NJ-semicommutative ring is NJ-abelian, much like every semicommutative ring is abelian.
New York Business Global LLC
Title: NJ-Abelian Rings: an Abelian-Like Approach
Description:
This article extends the concept of NJ-semicommutative rings to introduce the broader class of NJ-abelian rings, which are defined by properties involving nilpotent elements and the Jacobson radical.
We investigate the unique algebraic properties of NJ-abelian rings and analyze their relationships with various types of rings, including abelian, reduced, J-clean, local, and Dedekind-finite rings.
In particular, we show that every NJ-semicommutative ring is NJ-abelian, much like every semicommutative ring is abelian.
Related Results
Effects of cleaning in Saturn's rings
Effects of cleaning in Saturn's rings
Saturn's rings are well known for many good reasons, one of them being their brightness. Made of almost 99% water ice, they are by far the most ice-rich object of the solar system,...
Quasi-semi clean rings
Quasi-semi clean rings
Recently, Tang et al. [1] studied a broader concept than the concept of clean rings called quasi-clean rings. In this paper, we use the method of Tang et al. [1] in generalizing cl...
Dreipassen – en magisk genstand?
Dreipassen – en magisk genstand?
The trefoil – a magical object?In 1997, a trefoil was found in a cremation pit at Bilstrup near Skive in Viborg county. The other grave goods, comprising fragments of arm rings and...
Gauge Theories in Rainbow Space-Time
Gauge Theories in Rainbow Space-Time
We construct Maxwell and Yang-Mills theories in the rainbow space-time. We show that the time-dependent Aharonov-Bohm phases for both Abelian and non-Abelian gauge fields are non-z...
The Removal Lemma: algebraic versions and applications
The Removal Lemma: algebraic versions and applications
This thesis presents some contributions in additive combinatorics and arithmetic Ramsey theory. More specifically, it deals with the interaction between combinatorics, number theor...
Characterizing asymptotic randomization in abelian cellular automata
Characterizing asymptotic randomization in abelian cellular automata
Abelian cellular automata (CAs) are CAs which are group endomorphisms of the full group shift when endowing the alphabet with an abelian group structure. A CA randomizes an initial...
A Kurosh-Amitsur Completely Prime Radical for Near-rings
A Kurosh-Amitsur Completely Prime Radical for Near-rings
Two generalizations of the completely prime radical of rings to near-rings, namely the completely prime radical of near-rings and the completely equiprime radical of near-rings wer...
Etruscan and South Italian Finger Rings in Oxford
Etruscan and South Italian Finger Rings in Oxford
Of the many benefactions to the University of Oxford made by Charles Drury Edmond Fortnum (1820–99) one of the most important but least publicised was his great collection of finge...