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Finite rings of principal ideals [PDF]
Mathematical Notes of the Academy of Sciences of the USSR, 1972 We investigate a class of finite rings of principal ideals: we derive the necessary and sufficient conditions that the rings of this class are uniquely defined by certain parameters to within an isomorphism.
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The American Mathematical Monthly, 2005
(2005). A (K)-Ring Satisfying the Ascending Chain Condition on Principal Ideals That Is Not a Principal Ideal Ring. The American Mathematical Monthly: Vol. 112, No. 6, pp. 523-524.
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(2005). A (K)-Ring Satisfying the Ascending Chain Condition on Principal Ideals That Is Not a Principal Ideal Ring. The American Mathematical Monthly: Vol. 112, No. 6, pp. 523-524.
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Modules Over Principal Ideal Rings
2021One result that greatly simplifies undergraduate linear algebra is that vector spaces over a field have a basis. This allows us to perform computations in coordinates, as well as to representat linear maps by matrices. Over a ring which is not a field, there exist modules which are not free, and the classification of modules over general rings is much ...
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Polynomial codes and principal ideal rings
Proceedings of IEEE International Symposium on Information Theory, 2002Conditions are given which determine when the ring R=S[x/sub 1/, ..., x/sub n/]/(f/sub 1/(x/sub 1/), ..., f/sub n/(x/sub n/)) is a principal ideal ring where either S=Z/sub m/ and R is finite or S is a field. If S and R are both finite then an ideal C of R is a linear code.
Andrei V. Kelarev, J. Cazaran
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Restricted left principal ideal rings
Israel Journal of Mathematics, 1972A ring is an LD-ring ifR is left bounded, ifR/J is a left Artinian left principal ideal ring for every proper idealJ inR, and ifR has finite left Goldie dimension. IfR is non-Artinian thenR is an order in a simple Artinian ringS. The ideal theory of LD-rings is investigated, and we discuss some conditions under which an LD-ring is an hereditary ring ...
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Rings with projective principal right ideals
Ukrainian Mathematical Journal, 1990It has been proved that if A is a right-distributive ring, algebraic over its center, and whose principal ideals are projective, then A is a left-distributive ring.
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On a problem in the theory of rings of principal ideals
Mathematical Notes of the Academy of Sciences of the USSR, 1974We give a negative answer to a question posed by A. V. Jategaonkar: is it not true that an arbitrary primary principal left ideal ring is a factor of a prime principal left ideal ring? We give a counter example in the class of finite complete primary principal ideal rings, the so-called Galois-Eisenstein-Ore rings.
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On Rings Whose Reflexive Ideals are Principal
Communications in Algebra, 2010We call a prime Noetherian maximal order R a pseudo-principal ring if every reflexive ideal of R is principal. This class of rings is a broad class properly containing both prime Noetherian pri-(pli) rings and Noetherian unique factorization rings (UFRs).
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