Results 31 to 40 of about 39,950 (199)

A weak periodicity condition for rings

International Journal of Mathematics and Mathematical Sciences, 2005
A ring is called semi-weakly periodic if each element which is not in the center or the Jacobson radical can be written as the sum of a potent element and a nilpotent element.
Hazar Abu-Khuzam, Howard E. Bell, Adil Yaqub   +2 more
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The Strongly Nil-Clean Rings Of Order Two Units [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics
If every element of a ring R is the sum of idempotent and nilpotent that commute, then the ring is said to be a strongly nil-clean. Further features of a strongly nil-clean ring are given in this paper.
Samira Toma, Nazar Shuker
doaj   +1 more source

On Generalized PF – Rings [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics, 2004
The aim of this paper is to extend several known results on GPF –rings. π-regular rings, PF-rings and GP-ideals are also considered. Among other results we prove that: If R is a uniform ring, then R is a GPF-ring if and only if every element of R is ...
Nazar Shuker, Husam Mohammad
doaj   +1 more source

Nilpotent elements in physics [PDF]

Journal of Physical Studies, 2007
Institute of Theoretical Physics, University of Wroclaw,pl. M. Borna 9, 50–204 Wroclaw, Poland(Received January 4, 2007)We briefly review some issues of the nilpotent objects in theoretical physics using simple modelsas an illustration. Nilpotent elements appear at quantum and classical level in several ways.
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On the generalization of pseudo p-closure in pseudo BCI-algebras [PDF]

Journal of Hyperstructures
In this paper, the notion of generalization of pseudo p-closure, denoted by gcl, is introduced and its related properties are investigated. The gcl of subalgebras and pseudo-ideals is discussed.
Padena Pirzadeh Ahvazi, Habib Harizavi, Tayebeh Koochakpoor   +2 more
doaj   +1 more source

Unit-Regularity of Regular Nilpotent Elements [PDF]

Algebras and Representation Theory, 2016
Let $a$ be a regular element of a ring $R$. If either $K:=\rm{r}_R(a)$ has the exchange property or every power of $a$ is regular, then we prove that for every positive integer $n$ there exist decompositions $$ R_R = K \oplus X_n \oplus Y_n = E_n \oplus X_n \oplus aY_n,$$ where $Y_n \subseteq a^nR$ and $E_n \cong R/aR$.
openaire   +3 more sources

On Clean and Nil-Clean Symbolic 2-Plithogenic Rings [PDF]

Neutrosophic Sets and Systems, 2023
A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a
P. Prabakara, Florentin Smarandache
doaj  

Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents

, 2014
We derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g.
De Sole, Alberto, Kac, Victor G., Valeri, Daniele   +2 more
core   +1 more source

The Nilpotent Regular Element Problem [PDF]

Canadian Mathematical Bulletin, 2016
AbstractWe use George Bergman’s recent normal form for universally adjoining an inner inverse to show that, for general rings, a nilpotent regular element x need not be unit-regular. This contrasts sharply with the situation for nilpotent regular elements in exchange rings (a large class of rings), and for general rings when all powers of the nilpotent
Pere Ara, Kevin C. O’Meara
openaire   +1 more source

Regular Nilpotent Elements and Quantum Groups [PDF]

Communications in Mathematical Physics, 1999
23 pages, LaTeX ...
openaire   +2 more sources