A weak periodicity condition for rings

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. After discussing some basic properties of such rings, we investigate their commutativity behavior.

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p-Γ-Rings

GANIT Journal of Bangladesh Mathematical Society ◽

10.3329/ganit.v30i0.8497 ◽

1970 ◽

Vol 30 ◽

pp. 1-10

Author(s):

Md Mahbubur Rashid ◽

AC Paul

Keyword(s):

Key Words ◽

Jacobson Radical ◽

Subject Classification ◽

Radical Class ◽

Basic Properties

The purpose of this paper is to introduce p-Γ-rings and a few of their most basic properties. Then these have been applied to investigate whether the most important properties like commutativty, being radical class and some other characterizations are preserved under our defined p-Γ-rings. Mathematical subject classification-2000: 16N20, 16N99. Key words: Γ -rings, p-rings, Jacobson radical, Radical class, p-Γ -rings. DOI: http://dx.doi.org/10.3329/ganit.v30i0.8497 GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 1-10

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A note on r-precious ring

Journal of Algebra and Its Applications ◽

10.1142/s0219498821502315 ◽

2020 ◽

pp. 2150231

Author(s):

Nitin Bisht

Keyword(s):

Regular Element ◽

Nilpotent Element ◽

Idempotent Element ◽

Von Neumann ◽

Regular Elements ◽

Basic Properties ◽

Euclidean Domain ◽

Von Neumann Regular

An element of a ring [Formula: see text] is said to be [Formula: see text]-precious if it can be written as the sum of a von Neumann regular element, an idempotent element and a nilpotent element. If all the elements of a ring [Formula: see text] are [Formula: see text]-precious, then [Formula: see text] is called an [Formula: see text]-precious ring. We study some basic properties of [Formula: see text]-precious rings. We also characterize von Neumann regular elements in [Formula: see text] when [Formula: see text] is a Euclidean domain and by this argument, we produce elements that are [Formula: see text]-precious but either not [Formula: see text]-clean or not precious.

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On Generalized Periodic-Like Rings

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2007/29513 ◽

2007 ◽

Vol 2007 ◽

pp. 1-5 ◽

Cited By ~ 1

Author(s):

Howard E. Bell ◽

Adil Yaqub

Keyword(s):

Jacobson Radical ◽

Opposite Parity ◽

Basic Properties ◽

Nilpotent Elements ◽

Positive Integers

LetRbe a ring with centerZ, Jacobson radicalJ, and setNof all nilpotent elements. CallRgeneralized periodic-like if for allx∈R∖(N∪J∪Z)there exist positive integersm,nof opposite parity for whichxm−xn∈N∩Z. We identify some basic properties of such rings and prove some results on commutativity.

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Direct sums ofJ-rings and radical rings

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171295000664 ◽

1995 ◽

Vol 18 (3) ◽

pp. 531-534

Author(s):

Xiuzhan Guo

Keyword(s):

Jacobson Radical ◽

Nilpotent Element ◽

Direct Sums

LetRbe a ring,J(R)the Jacobson radical ofRandPthe set of potent elements ofR. We prove that ifRsatisfies(∗)givenx,yinRthere exist integersm=m(x,y)>1andn=n(x,y)>1such thatxmy=xynand if eachx∈Ris the sum of a potent element and a nilpotent element, thenNandPare ideals andR=N⊕P. We also prove that ifRsatisfies(∗)and if eachx∈Rhas a representation in the formx=a+u, wherea∈Pandu∈J(R),thenPis an ideal andR=J(R)⊕P.

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J-Boolean group rings and skew group rings

Journal of Algebra and Its Applications ◽

10.1142/s0219498818502109 ◽

2018 ◽

Vol 17 (11) ◽

pp. 1850210

Author(s):

Dinesh Udar ◽

R. K. Sharma ◽

J. B. Srivastava

Keyword(s):

Jacobson Radical ◽

Group Rings ◽

Basic Properties ◽

Boolean Rings ◽

Skew Group Rings

A ring [Formula: see text] is called semiboolean if [Formula: see text] is boolean and idempotents lift modulo [Formula: see text], where [Formula: see text] denotes the Jacobson radical of [Formula: see text]. In this paper, we define [Formula: see text]-boolean rings as a generalization of semiboolean rings. A ring [Formula: see text] is said to be J-boolean if [Formula: see text] is boolean. Various basic properties of these rings are obtained. The [Formula: see text]-boolean group rings and skew group rings have been studied. It is investigated whether the results obtained for [Formula: see text]-boolean group rings also hold for the skew group rings.

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On the Essence and Tipology of International Public Goods

Voprosy Ekonomiki ◽

10.32609/0042-8736-2005-3-131-141 ◽

2005 ◽

pp. 131-141

Author(s):

V. Mortikov

Keyword(s):

Economic Policy ◽

Social Construction ◽

Public Goods ◽

Public Good ◽

Global Public Goods ◽

Club Goods ◽

Basic Properties ◽

International Public Goods ◽

Regional Public Goods ◽

Joint Products

The basic properties of international public goods are analyzed in the paper. Special attention is paid to the typology of international public goods: pure and impure, excludable and nonexcludable, club goods, regional public goods, joint products. The author argues that social construction of international public good depends on many factors, for example, government economic policy. Aggregation technologies in the supply of global public goods are examined.

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