Relevant bibliographies by topics / Non-unique factorization

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Non-unique factorization'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 February 2022

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Journal articles on the topic "Non-unique factorization"

1

Chang, Gyu Whan, and Andreas Reinhart. "Unique factorization property of non-unique factorization domains II." Journal of Pure and Applied Algebra 224, no. 12 (2020): 106430. http://dx.doi.org/10.1016/j.jpaa.2020.106430.

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Abbasi, G. Q., S. Kobayashi, H. Marubayashi, and A. Ueda. "Non commutative unique factorization rings." Communications in Algebra 19, no. 1 (1991): 167–98. http://dx.doi.org/10.1080/00927879108824136.

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Stein, S., and S. Szabó. "Elementary Infinite Sources of Non-Unique Factorization Rings." American Mathematical Monthly 101, no. 8 (1994): 769–70. http://dx.doi.org/10.1080/00029890.1994.11997023.

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Stein, S., and S. Szabo. "Elementary Infinite Sources of Non-Unique Factorization Rings." American Mathematical Monthly 101, no. 8 (1994): 769. http://dx.doi.org/10.2307/2974531.

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Mihet, Dorel. "A note on non-unique factorization domains (UFD)." Resonance 15, no. 8 (2010): 737–39. http://dx.doi.org/10.1007/s12045-010-0083-8.

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Marcelo, Agustin, and Peter Schenzel. "Non-Cohen–Macaulay unique factorization domains in small dimensions." Journal of Symbolic Computation 46, no. 5 (2011): 609–21. http://dx.doi.org/10.1016/j.jsc.2010.10.010.

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Chapman, Scott T. "A Simple Example of Non-Unique Factorization in Integral Domains." American Mathematical Monthly 99, no. 10 (1992): 943. http://dx.doi.org/10.2307/2324487.

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Chapman, Scott T. "A Simple Example of Non-unique Factorization in Integral Domains." American Mathematical Monthly 99, no. 10 (1992): 943–45. http://dx.doi.org/10.1080/00029890.1992.11995958.

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Maoying, Qiao, Yu Jun, Liu Tongliang, Wang Xinchao, and Tao Dacheng. "Diversified Bayesian Nonnegative Matrix Factorization." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 5420–27. http://dx.doi.org/10.1609/aaai.v34i04.5991.

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Nonnegative matrix factorization (NMF) has been widely employed in a variety of scenarios due to its capability of inducing semantic part-based representation. However, because of the non-convexity of its objective, the factorization is generally not unique and may inaccurately discover intrinsic “parts” from the data. In this paper, we approach this issue using a Bayesian framework. We propose to assign a diversity prior to the parts of the factorization to induce correctness based on the assumption that useful parts should be distinct and thus well-spread. A Bayesian framework including this
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10

Gilchrist, Martin. "Non-commutative Noetherian Unique Factorization Domains often have stable range one." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 2 (1989): 229–35. http://dx.doi.org/10.1017/s030500410007804x.

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Let R be a Noetherian ring. If R is commutative then (a) every non-unit is contained in a height-1 prime ideal - this is the Krull principal ideal theorem - but (b) R can have an arbitrarily large stable range. The main aim of this paper is to show that if certain non-commutative rings satisfy condition (a) then they have stable range one. We shall prove theTheorem. Let R be a Noetherian domain which is not commutative. Suppose that every non-unit of R lies in at least one height-1 prime ideal and that every height-1 prime is completely prime. Then the stable range of R is one.
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Dissertations / Theses on the topic "Non-unique factorization"

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Antoniou, Austin A. "On Product and Sum Decompositions of Sets: The Factorization Theory of Power Monoids." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1586355818066608.

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Laska, Jason A. "On Conjectures Concerning Nonassociate Factorizations." 2010. http://trace.tennessee.edu/utk_graddiss/818.

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We consider and solve some open conjectures on the asymptotic behavior of the number of different numbers of the nonassociate factorizations of prescribed minimal length for specific finite factorization domains. The asymptotic behavior will be classified for Cohen-Kaplansky domains in Chapter 1 and for domains of the form R=K+XF[X] for finite fields K and F in Chapter 2. A corollary of the main result in Chapter 3 will determine the asymptotic behavior for Krull domains with finite divisor class group.
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Lynch, Benjamin Ryan. "Elasticity of Krull Domains with Infinite Divisor Class Group." 2010. http://trace.tennessee.edu/utk_graddiss/821.

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The elasticity of a Krull domain R is equivalent to the elasticity of the block monoid B(G,S), where G is the divisor class group of R and S is the set of elements of G containing a height-one prime ideal of R. Therefore the elasticity of R can by studied using the divisor class group. In this dissertation, we will study infinite divisor class groups to determine the elasticity of the associated Krull domain. The results will focus on the divisor class groups Z, Z(p infinity), Q, and general infinite groups. For the groups Z and Z(p infinity), it has been determined which distributions of
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Books on the topic "Non-unique factorization"

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1944-, Halter-Koch Franz, ed. Non-unique factorizations: Algebraic, combinatorial and analytic theory. CRC Press, 2005.

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2

Geroldinger, Alfred, and Franz Halter-Koch. Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory. Taylor & Francis Group, 2006.

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Geroldinger, Alfred, and Franz Halter-Koch. Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory (Pure and Applied Mathematics). Chapman & Hall/CRC, 2006.

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Book chapters on the topic "Non-unique factorization"

1

"Concepts in factorization theory and examples." In Non-Unique Factorizations. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420003208-6.

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"Concepts in factorization theory and examples." In Non-Unique Factorizations. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420003208.ch1.

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Anderson, Daniel. "Non-Atomic Unique Factorization in Integral Domains." In Arithmetical Properties of Commutative Rings and Monoids. CRC Press, 2005. http://dx.doi.org/10.1201/9781420028249.ch1.

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"Additive group theory." In Non-Unique Factorizations. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420003208-10.

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"Arithmetical invariants of Krull monoids." In Non-Unique Factorizations. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420003208-11.

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"Global arithmetic of Krull monoids." In Non-Unique Factorizations. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420003208-12.

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"Abstract analytic number theory." In Non-Unique Factorizations. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420003208-13.

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"Analytic theory of non-unique factorizations." In Non-Unique Factorizations. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420003208-14.

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"Algebraic theory of monoids." In Non-Unique Factorizations. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420003208-7.

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"Arithmetic theory of monoids." In Non-Unique Factorizations. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781420003208-8.

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Conference papers on the topic "Non-unique factorization"

1

Song, Hyeonik, and Katherine Fu. "Approaches for Supporting Exploration for Analogical Inspiration With Behavior, Material and Component Based Structural Representations of Patent Databases." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85591.

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This paper presents an explorative-based computational methodology to aid the analogical retrieval process in design-by-analogy practice. The computational methodology, driven by Non-negative Matrix Factorization (NMF), iteratively builds a hierarchical repositories of design solutions within which clusters of design analogies can be explored by designers. In the work, the methodology has been applied on a large repository of mechanical design related patents, processed to contain only component-, behavior-, or material-based content, to demonstrate that unique and valuable attribute-based ana
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