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Commutative Rings With Two-Absorbing Factorization

Thesis Info

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Author

Mukhtar, Muzammil

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2018

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/12905/1/Muzammil_Mukhtar_Maths_HSR_2018_GCU_Lahore_31.07.2018.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725749004

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In this thesis we introduce and study the concept of a TAF-ring: a ring whose ideals are fnite products of 2-absorbing ideals. Following Badawi [7], an ideal I of a commutative ring R is a 2-absorbing ideal if whenever a; b; c ϵ R and abc ϵ 2 I, then ab ϵ I or ac ϵ I or bc ϵ I.
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مولانابدر الدین علوی

مولانا بدر الدین علوی
افسوس ہے کہ گذشتہ مہینے مولانا بدرالدین صاحب علوی سابق استاد عربی مسلم یونیورسٹی نے وفات پائی مرحوم استاد العلماء مولانا لطف اﷲ صاحب علی گڑھی کے تلمیذ رشید اور مولانا حبیب الرحمن خاں شروانی مرحوم کے ہمدرس تھے، ان کی پوری زندگی درس و تدریس اور علم و ادب کی خدمت میں گذری مسلم یونیورسٹی سے ریٹائر ہونے کے بعد گھر پر عربی کے شایقین کو درس دیتے تھے، انھوں نے عرصہ ہوا المختار بن شعر بشار بن برد پر اور اس کی شرح لابی الطاہر اسمٰعیل بن احمد التجیبی بڑے اہتمام سے تصحیح و تحشیہ کے ساتھ شائع کیا اﷲ تعالیٰ اس شیدائے علم کی مغفرت فرمائے۔
(شاہ معین الدین ندوی،مارچ ۱۹۶۵ء)

عمومی اسباب طلاق اور ان کا حل پاکستانی معاشرے میں

Happy life with chest and purity by the way of NIKAH is based on best marital relationships. If there is no mutual love, affection and complete harmony in the marriage life, then the life of wife and husband become very difficult to maintain. This is one of the key feature of Islam that it has made humans responsible for mutual rights and responsibilities and bound them to follow rules and regulations. By doing so the decent nations of the whole world either Muslims or non-Muslims can achieve countless benefits of the marital status. Therefore, the divorce which the messenger of Allah (peace and blessing of Allah be upon Him) has declared as “Most hated act” in lawful and legitimate acts near the Almighty Allah, must be avoided, even if potential or should be minimized in our society. There are many causes of divorce in our Pakistani society and among the significant lake of proper religious education and guidance, family and domestic disputes, complex judicial system, exchange marriage, negative role of media, adverse effects of cellular phones, improper usage of Internet, extreme and excessive use of social media, second marriage, undue obedience of parents and drug addiction are included. This article not only indicates the significant causes of divorce in Pakistani society but also describes the details of their procurement. If corrective measures are taken for these root causes, there is a high hope that the divorce rate will be clearly reduced.

New Great Game in Central Asia: Convergence and Divergence Among Russia, China and Usa

Central Asia and Afghanistan has been the hub of international power politics among the big powers. The ―Great Game‖ there came to an end with the disintegration of Soviet Union - creating power vacuum in the region. The big powers rushed to occupy the space so that it may not be occupied by rivals. In this way a competition started among them for different competing interests known as new ―Great Game‖. Geographic and strategic location, energy resources, market and raw material in the region have been driving forces behind the renovated interests of the big powers and their convergence and divergence in the region‘s geopolitics.Through the application of Neo-realist approach, this research has analyzed the significance of the region and competition and cooperation among Russia, China and USA. It has analyzed how big powers interests have converged and diverged in CARs and Afghanistan‘s Geo-politics and the logic behind it. The main factors of divergence among the three are related to energy and its transportation routes, market,raw materials, land route between eastern and eastern world, strategic location and its role in bringing changes in the international system and US penetration into CARs and Afghanistan militarily.It has been concluded by stating that what strategies the big powers are applying for attainment, keeping and enhancement of power. The energy resources of the region are considered the means for achieving these exalted interests. It has also been concluded by stating that though the big powers behave aggressively and self-interestedly with each other but they may have a minimum degree of cooperation to deal with shared concerns such as terrorism, separatism, poverty, smuggling, illiteracy and drug and human trafficking. It has been predicted that hot war among them does not seem possible because their interests are mostly connected with the hydrocarbon resources of the region, its infrastructure, market and raw material. In case of war the infrastructure of the energy resources and market would be destroyed and the region would face destabilization. Furthermore, all the big powers are atomic acting as a deterrent among them. Presently, the region is dominated economically by China and politically by Russia and US is struggling to mitigate the influence of Russia and china in the region. Changing geopolitical scenario of the region and shifts in the loyalties and interests of the CARs and Afghanistan may change it. The CARs to materialize its interests are using strategies such as multi-vector approach, balancing and counterbalancing, playing big powers against each other.