Results 321 to 330 of about 4,472,960 (363)
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Rank-Metric Codes Over Finite Principal Ideal Rings and Applications
IEEE Transactions on Information Theory, 2019In this paper, it is shown that some results in the theory of rank-metric codes over finite fields can be extended to finite commutative principal ideal rings.
Hermann Tchatchiem Kamche +1 more
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ACM-SIAM Symposium on Discrete Algorithms, 2016
This paper gives polynomial time quantum algorithms for computing the ideal class group (CGP) under the Generalized Riemann Hypothesis and solving the principal ideal problem (PIP) in number fields of arbitrary degree.
Jean-François Biasse, F. Song
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This paper gives polynomial time quantum algorithms for computing the ideal class group (CGP) under the Generalized Riemann Hypothesis and solving the principal ideal problem (PIP) in number fields of arbitrary degree.
Jean-François Biasse, F. Song
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Ideals that are an irredundant union of principal ideals
Rendiconti del Circolo Matematico di Palermo, 2012We investigate ideals of a commutative ring that are an irredundant union of principal ideals. Special attention is paid to prime ideals that are a finite union of principal ideals.
Sangmin Chun, D. D. Anderson
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, 2018
Let D be an integral domain, ∗ a star-operation on D, and S a multiplicative subset of D. We define D to be an S-∗w-principal ideal domain if for each nonzero ideal I of D, there exist an element s...
Hwankoo Kim, J. Lim
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Let D be an integral domain, ∗ a star-operation on D, and S a multiplicative subset of D. We define D to be an S-∗w-principal ideal domain if for each nonzero ideal I of D, there exist an element s...
Hwankoo Kim, J. Lim
semanticscholar +1 more source
Abelian Codes in Principal Ideal Group Algebras
IEEE Transactions on Information Theory, 2013We study abelian codes in principal ideal group algebras (PIGAs). We first give an algebraic characterization of abelian codes in any group algebra and provide some general results.
Somphong Jitman +3 more
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Principal Borel ideals and Gotzmann ideals
Archiv der Mathematik, 2003In this paper we characterize all principal Borel ideals with Borel generator up to degree 4 which are Gotzmann. We also classify principal Borel ideals with a Borel generator of degree d which are lexsegment and we describe the shadows of principal Borel ideals. Finally, we discuss the corresponding results for squarefree monomial ideals.
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1988
The theory of modules over a principal ideal domain is closely related to the theory of vector spaces over a field and is almost identical to the theory of abelian groups, which are modules over the integers. The analogue of a finite-dimensional vector space is a finitely presented module over a principal ideal domain.
Fred Richman, Ray Mines, Wim Ruitenburg
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The theory of modules over a principal ideal domain is closely related to the theory of vector spaces over a field and is almost identical to the theory of abelian groups, which are modules over the integers. The analogue of a finite-dimensional vector space is a finitely presented module over a principal ideal domain.
Fred Richman, Ray Mines, Wim Ruitenburg
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2010
This chapter has very few definitions, but many results. In the first section we prove Krull’s principal ideal theorem, which says, roughly speaking, that an ideal generated by n elements has height at most n. This theorem is one of the workhorses of commutative algebra.
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This chapter has very few definitions, but many results. In the first section we prove Krull’s principal ideal theorem, which says, roughly speaking, that an ideal generated by n elements has height at most n. This theorem is one of the workhorses of commutative algebra.
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Full and Elementary Nets over the Quotient Field of a Principal Ideal Ring
Journal of Mathematical Sciences, 2018R. Y. Dryaeva +2 more
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