| His early works range over number theory, statistics, combinatorics, game theory, as well as his principal interest of commutative algebra. |
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| In the 1840s, the Irish mathematician William Hamilton found that multiplication was not commutative in all number systems. |
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| Using the fact that polynomial rings are Noetherian, show that every finitely generable commutative ring is finitely presentable. |
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| An operation is commutative if you can change the order of the numbers involved without changing the result. |
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| The second difficulty was more damaging and, to a degree, commutative with the first. |
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| These two rules are called the commutative and associative laws for multiplication. |
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| What are the associative, commutative, distributive, and equality properties? |
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| Homomorphic mappings of rings into fields are very common in commutative algebra and in its applications. |
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| Of course, the relationship between painting and philosophy is not entirely commutative. |
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| The different forms of economic enterprise to which they give rise find their main point of encounter in commutative justice. |
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| Community life is not built on a base of mere commutative justice but rather in accord with distributive justice. |
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| This is a consequence of large rotations not being commutative in three dimensions, so the averages are not accurate in regions of high variability. |
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| In the density-independent case, this multiplication is commutative. |
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| The commutative law does not necessarily hold for multiplication of conditionally convergent series. |
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| So, the addition and multiplication we are used to using are commutative. |
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| The associative, commutative, and distributive laws of elementary algebra are valid for the dot multiplication of vectors. |
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| Addition and multiplication are commutative operations but subtraction and division are not. |
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| An abelian group is a group whose operation is commutative. |
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| The market is subject to the principles of socalled commutative justice, which regulates the relations of giving and receiving between parties to a transaction. |
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| In relation to the multiplication operation with modulo-r reduction, the form a finite commutative group closed on itself, that is to say their products remain in the set. |
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| In synallagmatic commutative contracts it is exceptional for the parties to agree that what is to be given in return is for the benefit of a third party. |
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| Living abroad is no problem for you and you have commutative skills. |
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| A lack of equivalence in the agreed contents of the obligations in a commutative contract is not a ground of annulment except where the law allows rescission of the contract by reason of substantive inequality of bargain. |
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| Since the AND logical operator is commutative, associative, and idempotent, then it distributes with respect to itself. |
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| The classical ring of quotients of a commutative Bezout ring is a regular local ring if and only if R is a commutative semihereditary local ring. |
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| Foster, The idempotent elements of a commutative ring form a Boolean Algebra, Duke math. |
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| Readers should have a background in number theory, commutative algebra, and the general theory of schemes. |
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| Among the topics are commutative topological groups, locally convex spaces and semi-norms, Hahn-Banach theorems, barreled spaces, closed graph theorems, and reflexivity. |
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| It asks standard, commutative and division questions to make sure that children develop a thorough understanding of these fundamental building blocks of maths. |
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| In Section 2 we give the basic definitions for matroids over a commutative ring, including representability, and we explain how they generalize the classical ones. |
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| Justice, although it be but one entire virtue, yet is described in two kinds of spices. The one is named justice distributive, the other is called commutative. |
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| Direct product decomposition of commutative semisimple rings, Proc. |
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| The PWA operator is monotonic, commutative, bounded and idempotent. |
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| Chapters address group theory, commutative rings, Galois theory, noncommutative rings, representation theory, advanced linear algebra, and homology. |
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| Commutative justice relates to the exchange of one thing for another, and is bottomed on the principle of something for something, or as the lawyers say, quid pro quo. |
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