Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMaximal Elements and Prime Elements in Lattice Modules
العناصر الأعظمية و العناصر الأولية في المقاسات الشبكية
1269
0 34
0
(
0
)
Added by
Damascus University ورقة بحثية
Publication date
2003
fields
Mathematics
and research's language is
العربية
Authors
إيمان الخوجة( باحث )
Created by
Shamra Editor
Ask ChatGPT about the research
درسنا في هذا البحث العلاقة بين العناصر الأعظمية (الأولية) في المقاس الـشبكي M و العناصـر الأعظمية (الأولية) في الشبكة الضربية L ، و برهنا أنه إذا كانت الـشبكة الـضربية L موضـعية و كـان العنصر الأكبر في M رئيسياً ضعيفاً فإن M يكون موضعياً أيضاً. كما عرفنا جذر جاكبسون في المقـاس M))M(J) و درسنا علاقته بجذر جاكبسون في الشبكة L))L(J.
In this paper we study the relationship between the maximal (prime) elements of M and the maximal (prime) elements of L. We show that, if L is a local lattice and the greatest element of M is weak principal, then M is local . Then we define the Jacobson radical of M and denote it by J(M) and we study its relationship with the Jacobson radical of L (J(L)) . Afterwards, we define the semiprime element in a lattice module M, and we show that the definitions of prime element and semiprime element are equivalent when the greatest element of M is multiplication and we study the properties equivalent to the properties of prime element in lattice module .
References used
DILWORTH, R. P. 1962. Abstract commutative ideal theory, pacific J. Math ., 12 , 481 – 498
JOHNSON, J. A. 1970. a–adic completions of Noetherian lattice modules. Fund. Math., 66, 341 – 371
JOHNSON, E. W. and JOHNSON, J. A. 1970. Lattice modules over semi–local Noether lattices. Fund. Math., 68, 187–201
rate research
Read More
In ١٩٦٢ R.P.Dilworth introduced the concept of a Noether lattice as an
abstraction of the concept of the lattice of ideals of a Noetherian ring. He
showed that many of the important theorems of classical ideal theory held in
them.
The purpose of
this paper is to introduce and study the concept of
idempotent elements for the multiplicative lattices , since they play very
idempotent role for studying the multiplicative lattices and some rings.
the research aims to know the methods of Landscape
Architecture, and to choose the green elements appropriate for them,
this can be achieved after knowing the climatic conditions that
prevail in different regional in general and in the Syrian Arab
Republic in Particular.
This research aims to study the effect of adding alloying elements and heat treatment
of Zinc metal on solar energy absorbing , nine alloys ingots were manufactured by
changing the percentages of added Aluminum and Copper on the pure Zinc, and thes
e
ratios of Aluminum were : (10% , 20% , 30% , 40 % , 50%) to demonstrate the effect of
adding Aluminum to Zinc metal on solar energy absorbing , and ratios of copper were :
(20% , 40%) , as well as we prepare two pure zinc samples with 99.2% of purity , one
was rapidly cooled and the other slowly cooled , to demonstrate the effect of heat treatment
on solar energy absorbing .
In order to measure the solar energy absorbing for prepared samples , we
manufactured a device depends on the methods of heat exchange between solar radiation
and the surface exposed to radiation .
The obtained results showed that adding Aluminum and Copper to the pure Zinc
caused a decrease in solar energy absorbing .
As well as increasing the percentages of adding Aluminum and Copper to the pure
Zinc caused a gradually decrease in solar energy absorbing .
comparing the absorbing of pure zinc samples, one was rapidly cooled and the other
slowly cooled , the results showed that the sample was rapidly cooled was better than the
sample slowly cooled on solar energy absorbing .
A Lie algebra g over a field F is a vector space together with a bilinear
map [ , ] satisfying [x ,x ] = 0 in addition to Jacobi identity . A Lie subalgebra
B of a Lie algebra g is said to be a Cartan subalgebra if it is a nilpotent and
equals its
normalizer, and it is proved that semi simple Lie algebra g
decomposes into weight spaces for B.
In this scientific paper we present the conception of distinguished
element 0 h in finite dimensional semi simple Lie algebra over a field F has
characteristic 0 and we will prove that the previous decomposition g into
weight spaces for B is the same to decomposition g as a direct sum of h0 ad eigen
spaces. This leads us to construct algorithm to test simple Lie algebras.
We programmed the previous algorithm to test simple linear Lie algebras
over a numeral field by Mathematica 5.0 program where applied this algorithm
on semi simple linear Lie algebra SL(3, ) to prove that it is simple.
This study was conducted in Syria Street, which connects between Yemen Square
and Republic Square in Latakia City. This paper cares to analyze arboreal rows in SYRIA
Street and to study their relation with the service and structural engineering com
ponents Of
that street . Moreover, the ideal state of these street trees was evaluated .Results of this
paper revealed, that the arboreal rows contain two botanic species (Ficus nitida L,
Jacaranda mimosaefolia Don.), which served to furnish the street with monotonic beauty
and humility in botanic diversity,and prominent breaks in these rows. Findings showed an
ideal decrease in the value of the two used botanic species where (Ficus nitidia) attained a
mark of 6.8/10 and (Jacaranda mimosaefolia) 6.34/10 . Corresponding to the relation of
trees to some street engineering elements, results indicated inobservance of standard
dimensions between planted trees and service elements. which negatively influenced the
aesthetic and position value of buildings’ and stores’ facets and guiding signs and
billboards on the one hand, and risk increase on pedestrians and vehicles due to blocking
vision of traffic signs and overlap of tree crowns with electricity and lighting posts on the
other hand.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
