Let  be a ring with identity. Recall that a submodule  of a left -module  is called strongly essential if for any nonzero subset  of , there is  such that , i.e., . This paper introduces a class of submodules called se-closed, where a submodule  of  is called se-closed if it has no proper strongly essential extensions inside . We show by an example that the intersection of two se-closed submodules may not be se-closed. We say that a module  is have the se-Closed Intersection Property, briefly se-CIP, if the intersection of every two se-closed submodules of  is again se-closed in . Several characterizations are introduced and studied for each of these concepts. We prove for submodules  and  of  that a module  has the

A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.

The group for the multiplication of closets is the set G|N of all closets of N in G, if G is a group and N is a normal subgroup of G. The term “G by N factor group” describes this set. In the quotient group G|N, N is the identity element. In this paper, we procure K(SL(2,125)) and K(SL(2,3125)) from the character table of rational representations for each group.

Facts and information contained showing in axes Find Egyptian Ottoman relations
(1863-1879), has gone through stages varying between tides, has witnessed the Khedive
Ismail three sultans Ottomans were Abdul Aziz Murad V, Abdul Hamid II, and since the
Khedive Ismail to judge sought to expand independence Egypt access to many privileges of
the sovereign on Egypt Ottoman Empire, in order to reach the country to independence, has
been chosen by the payment of money and gifts to gain independence, without resorting to
arms, and from this point of Khedive make a lot of money to get the privileges, the state of
the Ottoman were not to issue Farmans but against the huge amounts of money, and as a
result of that policy got

In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.

الخلاصة Bahraini Parliamentary Elections and their Impact on the Popular Uprising) Bahrain has a distinguished constitutional and parliamentary experience, which distinct it from the other Gulf Cooperation Council (GCC) countries. Its experience in this area is the second after the experience of Kuwait to establish a system of government based on modern constitutional principles. As the government presented the Constitution to the Constituent Assembly elected by people and approved in 09/06/1973. After that, it witnessed the birth of the first parliament elected by the people in 1973, but the experiment did not last long and the parliament dissolved by Prince, and didn’t determine the period of the return of the working with the

 This research test the relationship and the effect of an explanatory variable transparency in the organizational reputation responder variable by senior management in the departments of the Ministry of Housing and Construction centrally funded, As well as come  out among other recommendations contribute to the achievement of organizational reputation of the organizations surveyed. Given the importance of the research topic for the public sector and the community and the environment in which they operate researcher designed questionnaire containing (30) items, and collected data from (92) respondents, representing the research community (eight establishments) exclusively and comprehensively, relying descriptive analytic