scholarly journals p-Γ-Rings

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

scholarly journals On Generalized Periodic-Like Rings

2007 ◽  
Vol 2007 ◽  
pp. 1-5 ◽  
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.

RADICALS WITH THE α-AMITSUR PROPERTY

2008 ◽  
Vol 07 (03) ◽  
pp. 347-361 ◽  
Author(s):  
SODNOMKHORLOO TUMURBAT ◽  
ROBERT WISBAUER
Keyword(s):  
Jacobson Radical ◽  
Radical Class ◽  
Prime Rings ◽  
Nil Ring

A radical γ of rings is said to have the Amitsur property if for all rings A, γ(A[X]) = (γ(A[X]) ∩ A)[X]. Let Xα denote a set of indeterminates of cardinality α. We say that γ has the α-Amitsur property if for all rings A, γ(A[Xα]) = (γ(A[Xα]) ∩ A)[Xα]. We study properties of this type of radicals and show relationships with other known radicals for rings. A ring A is said to be an absolute γ-ring if A[x1,…, xn] ∈ γ, for any n ∈ ℕ. We show that A is an absolute 𝔾-ring for the Brown–McCoy radical 𝔾, if and only if A is in the radical class S determined by the unitary strongly prime rings. Moreover, A is an absolute nil ring if and only if A is an absolute J-ring, where J denotes the Jacobson radical.

scholarly journals Role and features of acoustic load in an ecological status

2014 ◽  
pp. 185-191
Author(s):  
L. Gileta
Keyword(s):  
Key Words ◽  
Noise Level ◽  
Acoustic Pressure ◽  
Ecological Status ◽  
Urban Ecosystem ◽  
Basic Properties ◽  
Acoustic Load

An acoustic load, which is one of the priority factors that affect the ecological status of a large urban ecosystem, that are territory of residence of the population – was considered. Basic properties of an acoustic pressure were determined. We differentiate the Lviv urban ecosystem from the acoustic geo systems as areas with approximate noise level and acoustic load centers. Key words: acoustic load, urban ecosystem, acoustic geo system.

scholarly journals The Jacobson Radical of the Endomorphism Semiring of P.Q.- Principal Injective Semimodules

2020 ◽  
Vol 17 (2) ◽  
pp. 0523
Author(s):  
Khitam Aljebory et al.
Keyword(s):  
Jacobson Radical ◽  
Subject Classification ◽  
Injective Semimodule

   In this work, we introduced the Jacobson radical (shortly Rad (Ș)) of the endomorphism semiring Ș =  ( ), provided that  is principal P.Q.- injective semimodule and some related concepts, we studied some properties and added conditions that we needed. The most prominent result is obtained in section three -If   is a principal self-generator semimodule, then (ȘȘ) = W(Ș). Subject Classification: 16y60

scholarly journals A weak periodicity condition for rings

2005 ◽  
Vol 2005 (9) ◽  
pp. 1387-1391
Author(s):  
Hazar Abu-Khuzam ◽  
Howard E. Bell ◽  
Adil Yaqub
Keyword(s):  
Jacobson Radical ◽  
Nilpotent Element ◽  
Periodicity Condition ◽  
Basic Properties

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.

scholarly journals The Jacobson semiradical over a certain semiring

2006 ◽  
Vol 37 (1) ◽  
pp. 67-76
Author(s):  
Huda Mohammed J. Al-Thani
Keyword(s):  
Left Ideal ◽  
Jacobson Radical ◽  
Ring Theory ◽  
Radical Class ◽  
Restricted Class ◽  
Proposition 8 ◽  
Direct Sum

The concept of the semiradical class of semirings was introduced in [3]. The purpose of this paper is to study one such semiradicals, the Jacobson semiradicals, over certain semirings. We generalize the concept of the Jacobson radical of a ring to a semiring. Some properties of the Jacobson semiradical $ JS(R) $ of the semiring $R$ parallel those of ring theory. In Section 1 we describe some preliminary definitions. In Section 2 we define regular strongly austere semimodulse. Theorem 1 characterizes a regular strongly austere semimodule in terms of a regular modular maximal subtractive left ideal. We define $JS(R)$ and derive some properties of this structure. In Section 3 we show that the $ JS(R) $ of a semiring has many representations as the intersection of left ideals. One of the more important of these is that $ JS(R) $ is the intersection of all left weakly primitive subtractive ideals. Proposition 6 characterizes a semiweekly primitive semiring in terms of a weakly primitive semiring. The interrelationships of strongly austere, weakly primitive and semiweekly primitive semirings are examined in Theorem 3. In Section 4, Proposition 7 shows that the $ JS(R) $ of a semiring with identity is the intersection of all regular maximal modular subtractive left ideals. Corollary 3 shows that $ JS(R) $ is the unique largest superfluous left ideal of $ R $. Proposition 8 shows that the class of Jacobson semiradical of semirings is closed under direct sum. We conclude with Section 5, a consideration of a certain restricted class of semirings. We show that the Jacobson semiradical for the semirings belonging to this class constitutes a semiradical class. Finally, Example 1 shows that a semiradical class need not be a radical class.

J-Boolean group rings and skew group rings

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.

C̆ech Fuzzy Soft Closure Spaces

2018 ◽  
Vol 7 (2) ◽  
pp. 62-74 ◽  
Author(s):  
Rasha Naser Majeed
Keyword(s):  
Topological Space ◽  
Subject Classification ◽  
Closure Space ◽  
Soft Sets ◽  
Basic Properties ◽  
Closed Mapping ◽  
Closure Spaces ◽  
Fuzzy Soft Sets ◽  
Soft Topological Space

In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.

Multislice imaging of gastrointestinal stromal tumors

2018 ◽  
pp. 3-14
Keyword(s):  
Computed Tomography ◽  
Key Words ◽  
Gold Standard ◽  
Gastrointestinal Stromal Tumors ◽  
Mesenchymal Tumors ◽  
Stromal Tumors ◽  
Preferential Localization ◽  
Multislice Imaging ◽  
Computed Tomography Diagnosis

Gastrointestinal stromal tumors (GIST) are the most common mesenchymal tumors of the digestive tract (1%). These tumors express the CD 117 in 95% of cases. The stomach is the preferential localization (70%). Diagnosis is difficult and sometimes late. Progress of imaging has greatly improved the management and the prognosis. Computed tomography (CT) is the gold standard for diagnosis, staging, and treatment follow-up. The increasing recognition of GIST’s histopathology and the prolonged survival revealed some suggestive imaging aspects. Key words: gastro-intestinal stromal tumors; computed tomography; diagnosis

METHODS OF CONSULTING ON STUDYING THE DEGREE OF MOISTURE SUPPLY OF SLOPE LANDS FOR AGRICULTURAL PRODUCTION IN AZERBAIJAN

2018 ◽  
Author(s):  
Prof.RAE Aliev Z.H.
Keyword(s):  
Key Words ◽  
Agricultural Production ◽  
Soil Ecology ◽  
Arable Soil ◽  
Clean Technology ◽  
Agricultural Product ◽  
Current Information ◽  
Moisture Supply ◽  
Managerial System

The current information on moisture and the temperature of the ground in managerial system by production to agricultural product necessary, in the first place, for taking the operative decisions at development ecological clean technology irrigation under growing agricultural cultures to achieve the maximum harvest. Key words: aerospace methods, COW, moisture, moisture test, arable, soil, ecology, vafer humidity, drill, graduation, tool, etc.

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