Ques:Information:  - A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br> It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox.  - Eben Matlis ( born 1923 ) is a mathematician known for his contributions to the theory of rings and modules , especially for his work with injective modules over commutative Noetherian rings , and his introduction of Matlis duality . Matlis earned his Ph.D. at the University of Chicago in 1958 , with Irving Kaplansky as advisor . He is now an emeritus professor at Northwestern University .  - In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module "Q" that shares certain desirable properties with the Z-module Q of all rational numbers. Specifically, if "Q" is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module "Y", then any module homomorphism from this submodule to "Q" can be extended to a homomorphism from all of "Y" to "Q". This concept is dual to that of projective modules. Injective modules were introduced in and are discussed in some detail in the textbook .  - Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.  - A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems.    'eben matlis' is related to which object entity through the relation of 'field of work'?  Choices: - algebra  - mathematician  - mathematics  - nature

Ans:algebra
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Ques:Information:  - The House of Medici was an Italian banking family, political dynasty and later royal house that first began to gather prominence under Cosimo de' Medici in the Republic of Florence during the first half of the 15th century. The family originated in the Mugello region of the Tuscan countryside, gradually rising until they were able to fund the Medici Bank. The bank was the largest in Europe during the 15th century, seeing the Medici gain political power in Florence  though officially they remained citizens rather than monarchs.  - Anna de ' Medici ( 31 December 1569 -- 19 February 1584 ) was the third child of Francesco I de ' Medici , Grand Duke of Tuscany , and Joanna of Austria . She was a member of the famous House of Medici .  - The Medici Bank (Italian: "Banco Medici") was a financial institution created by the Medici family in Italy during the 15th century (13971494). It was the largest and most respected bank in Europe during its prime. There are some estimates that the Medici family was, for a period of time, the wealthiest family in Europe. Estimating their wealth in today's money is difficult and imprecise, considering that they owned art, land, and gold. With this monetary wealth, the family acquired political power initially in Florence, and later in the wider spheres of Italy and Europe.  - Cosimo di Giovanni de' Medici (called 'the Elder' (Italian "il Vecchio") and, posthumously", "Father of the Nation' (Latin "pater patriae"); 10 April 1389  1 August 1464) was an Italian banker and politician, the first of the Medici political dynasty, "de facto" rulers of Florence during much of the Italian Renaissance. Despite his influence, his power was not absolute; Florence's legislative councils at times resisted his proposals, something which would not have been tolerated by the Visconti of Milan, for instance; throughout his life he was always "primus inter pares", or "first among equals". His power derived from his great wealth as a banker, and he was a great patron of learning, the arts and architecture.  - Florence is the capital city of the Italian region of Tuscany and of the Metropolitan City of Florence. It is the most populous city in Tuscany, with 383,083 inhabitants, expanding to over 1,520,000 in the metropolitan area.  - The Mugello is a historic region and valley in northern Tuscany, in Italy. It is located north of the Province of Florence and city of Florence.  - Francesco I (25 March 1541  19 October 1587) was the second Grand Duke of Tuscany, ruling from 1574 until his death in 1587. He was the second grand duke of the house of Medici.  - The Republic of Florence, also known as the Florentine Republic, was a medieval and early modern state that was centered on the Italian city of Florence in Tuscany. The republic originated in 1115, when the Florentine people rebelled against the Margraviate of Tuscany upon the death of Matilda, a woman who controlled vast territories including Florence. The Florentines formed a commune in her successors' place. The republic was ruled by a council, known as the signoria. The signoria was chosen by the "gonfaloniere" (titular ruler of the city), who was elected every two months by Florentine guild members.  - Europe is a continent that comprises the westernmost part of Eurasia. Europe is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, and the Mediterranean Sea to the south. To the east and southeast, Europe is generally considered as separated from Asia by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways of the Turkish Straits. Yet the non-oceanic borders of Europea concept dating back to classical antiquityare arbitrary. The primarily physiographic term "continent" as applied to Europe also incorporates cultural and political elements whose discontinuities are not always reflected by the continent's current overland boundaries.    'anna de' medici' is related to which object entity through the relation of 'place of birth'?  Choices: - atlantic ocean  - florence  - italy  - march  - most  - mugello  - of  - republic  - southeast  - time  - tuscany

Ans:
florence
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