Semirings, one of the most natural generalization of rings and distributive lattices, were first appeared in the study of ideals of rings, by Dedekind [25] and then Vandiver[78] formally introduced this notion, in 1934. One of the oldest algebraic structure, set of all natural numbers, is also a semiring. Over the years, tremendous applications of the theory of semirings have been recorded [33], from both domains of mathematics. Several types of semirings considered by researchers with respect to their applications in different areas including optimization theory, theoretical physics and computer sciences([1], [26], [30], [32], [77]). One of the most favorite type of semiring which was studied by algebraists during the last few years, is additively inverse semiring. The algebraic structure of inverse semiring was introduced by Karevellas[53] in 1973. In [9], Bandlet and Petrich characterized inverse semirings as a subdirect product of rings and distributive lattices. Sen[76], Ghosh[29] and Mukhopadhyay [74] and many others also considered the structure of inverse semiring. Recently, another class of semirings which appeared in the corpus, is the class of MA-Semirings. Javed, Aslam and Hussain[49] identified this class, as a subclass of additive inverse semirings which satisfies the condition (A-2) stated by Bandlet and Petrich in [9]. They initiated the theory of commutators with its fundamental identities in MA-Semirings, which later proved to be very fruitful in investigating many concepts of ring theory. These include theory of dependent elements and free actions[50], commutativity and centralizing mappings[51] and the theory of derivations of MA-Semirings[49]. Indeed, this algebraic structure is of considerable interest in targeting and generalizing many Lie type results of rings and algebra to semirings. As the name suggests, in this thesis, we will be considering MA-Semirings in regards of various concepts of ring theory. As usual, the first chapter will be devoted to preliminaries that includes some basic concepts of semiring theory. The chapter contains a brief introduction to the class of MA-Semirings and the notion of commutators in MA-Semirings. Chapter 2, deals with the theory of Lie and Jordan ideals of MA-Semirings. We introduce the notion of Jordan ideals of MA-Semiring and investigate famous results of Herstein[35, 40], in the setting of MA-Semirings. Lie ideals of MA-Semiring have been defined, already, by Javed and Aslam *51+. In this chapter, we explore Lanski*56+ and Herstein’s work*43+ on Lie ideals and extend their work to MA-Semirings. Some results of this chapter have accepted for the publication in the Italian Journal of Pure and Applied Mathematics[71]. In Chapter 3, we study the theory of derivation of MA-Semirings. In this regard, we probe the most investigated work of Posner on derivation of prime rings [66]. We also present the proof of one of the famous Posner’s theorem, namely, Posner’s second theorem of derivation, for MA-Semirings. The results of this chapter have accepted for the publication in Hacettepe Journal of Mathematics and Statistics[72]. Chapter 4, will be devoted to the study of Jordan Mappings in MA-Semirings. We formulate the notion of Jordan homomorphism and Jordan triple Homomorphism of MA-Semirings. A few well-known results obtained by Bre s ( ar[15] and Herstein[38], in this subject, are also generalized for MA-Semirings. In last two sections, we define Jordan derivation and Jordan triple derivation of MA-Semirings. In this chapter, we also prove that a Jordan derivation of 2-torsion free prime MA-Semiring is a derivation, which generalizes classical result of Bresar’s [13]. The contents of this chapter have published in the Journal of Open Mathematics[69]. In Chapter 5, we will study the most important concept of left centralizers on MA-Semirings. The work in this chapter, is motivated by the study of Zalar, Vukman and Bres ( ar [19, 79, 80, 84] on left centralizers. Most of the results of this chapter are part of our publication in the Journal of Quasigroups and related systems[70] and in the Journal of Discussiones Mathematicae-General Algebra and Applications[68]. In the last chapter, we will be considering MA-Semiring with the notion of dependent elements and free actions. In his Ph.D. thesis[50], Javed introduced the notions of dependent elements and free actions for the class of MA-Semirings. This chapter is devoted for the development of these notions. Results of this chapter have published in International Mathematical Forum [73].
The development of Islamic boarding schools is one of the targets for sharia economic development which is based on the understanding of the halal value chain where the development of Islamic economics and finance summarizes various initiative programs including the development of Islamic boarding schools. The purpose of this study is to describe how the implementation of the Islamic Boarding School Accounting Guidelines at Al Huda Islamic Boarding School which is more focused on the readiness of HR at Al Huda Islamic Boarding School in applying the Islamic Boarding School Accounting Guidelines. The Al Huda Islamic boarding school was chosen as the research locus because the Al Huda Islamic Boarding School was appointed by Bank Indonesia Gorontalo Representative Office as a pilot project for the Pesantren (Islamic Boarding School) which applies the Islamic Boarding School Accounting Guidelines. The stages of the research method began with observations and results of interviews with informants from the board of the Al-Huda Islamic Boarding School. The results showed that there was a desire to apply these guidelines in the Al-Huda Islamic boarding school. Even though treasurers, secretaries and operators do not have a basic knowledge of the Economics of Accounting, the existing human resources are ready to apply the Pesantren accounting guidelines, of course, adjusting to the needs of the Al-Huda Islamic boarding school. The author sees that there is no urgency in implementing Islamic boarding school accounting guidelines at the Al-Huda Islamic boarding school because the reporting entity is the foundation that houses the Al-Huda Islamic boarding school, the Al Huda Islamic Education and Da'wah Foundation, Gorontalo. The foundation is fully responsible for the donors or the community.
The discipline of Philosophy has always been widely encompassing inquiries from varied disciplines of both pure and social sciences; that is why now it includes almost every dimension of society. Pioneered in the Greek era, and evolved with the magnificent ancient historical foundations, Philosophy has gained worthy interdisciplinary vastness in 19th and 20th centuries. This thesis is an effort to explore Philosophy of cosmopolitan nationalism and its application in Sindh. This thesis discusses how the idea of nationalism has been critically evaluated as the world witnessed that the oppression under Hitler’s Nazism and Mussolini’s Fascism were also dubbed as nationalism. This damaged the justified and true nationalistic struggles of the beleaguered nations, of which Pakistan is the best example. This thesis is an effort to understand evolution of history, connotation and merits and demerits of cosmopolitan nationalism to comprehend the transformation of patriotic chronicles of Sindh’s political history into the precincts of cosmopolitan nationalism in Pakistan. Pakistan is a federation formed by the constituent units, in which the relationship between the units and the federation has always been estranged due to the thrust of the uniformity paradigm since the country’s inception, which cost division of the country in 1971. This thesis bases its main argument on Marxist perspective, which offers an enduring answer to the problems of Sindh by reforming its society with the help of class struggle as envisaged by Karl Marx and Fredrich Engels. The Marxist proposition of class struggle is judiciously used in the thesis; since Marx’s paradigm was universalistic, there is no doubt that in the present century cosmopolitan nationalism may take enormous benefit from Marxian paradigm in promoting class struggle to unite people of different ethnicities in Pakistan, as we observe this happening in the different parts of the world, particularly in the 20th century. The same can happen in Sindh as well. This especially is being done by some Marxist political activists in Pakistan, such as R. B. Palijo’s socialist paradigm in relation to Sindh province of Pakistan, to resolve tension between different ethnicities in the province of Sindh.