Srinivas, K.; Subramani, M.; Sangale, Usha K. Euclidean algorithm in Galois quartic fields. (English) Zbl 1518.11073 Rend. Circ. Mat. Palermo (2) 72, No. 1, 1-7 (2023). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11R16 11R04 PDFBibTeX XMLCite \textit{K. Srinivas} et al., Rend. Circ. Mat. Palermo (2) 72, No. 1, 1--7 (2023; Zbl 1518.11073) Full Text: DOI arXiv
Graves, Hester The minimal Euclidean function on the Gaussian integers. (English) Zbl 1504.13021 Indag. Math., New Ser. 34, No. 1, 78-88 (2023). Reviewer: Jebrel M. Habeb (Irbid) MSC: 13F07 11A05 PDFBibTeX XMLCite \textit{H. Graves}, Indag. Math., New Ser. 34, No. 1, 78--88 (2023; Zbl 1504.13021) Full Text: DOI arXiv
Afre, Naresh V.; Garge, Anuradha S. Gow-Tamburini type generation of \(\mathrm{SL}_3(R)\) over the rings of integers of imaginary quadratic number fields of class number one. (English) Zbl 1485.11153 Proc. Indian Acad. Sci., Math. Sci. 132, No. 1, Paper No. 26, 6 p. (2022). MSC: 11R04 11R11 13F07 PDFBibTeX XMLCite \textit{N. V. Afre} and \textit{A. S. Garge}, Proc. Indian Acad. Sci., Math. Sci. 132, No. 1, Paper No. 26, 6 p. (2022; Zbl 1485.11153) Full Text: DOI
Deshouillers, J.-M.; Gun, S.; Sivaraman, J. On Euclidean ideal classes in certain abelian extensions. (English) Zbl 1485.11154 Math. Z. 296, No. 1-2, 847-859 (2020). Reviewer: James E. Carter (Charleston) MSC: 11R20 11R29 11N36 PDFBibTeX XMLCite \textit{J. M. Deshouillers} et al., Math. Z. 296, No. 1--2, 847--859 (2020; Zbl 1485.11154) Full Text: DOI
Srinivas, Kotyada; Subramani, Muthukrishnan A survey of certain Euclidean number fields. (English) Zbl 1436.11127 Chakraborty, Kalyan (ed.) et al., Class groups of number fields and related topics. Collected papers presented at the first international conference, ICCGNFRT, Harish-Chandra Research Institute, Allahabad, India, September 4–7, 2017. Singapore: Springer. 57-65 (2020). MSC: 11R04 11A05 11R16 11-02 PDFBibTeX XMLCite \textit{K. Srinivas} and \textit{M. Subramani}, in: Class groups of number fields and related topics. Collected papers presented at the first international conference, ICCGNFRT, Harish-Chandra Research Institute, Allahabad, India, September 4--7, 2017. Singapore: Springer. 57--65 (2020; Zbl 1436.11127) Full Text: DOI
Prokip, V. M. On the divisibility of matrices with remainder over the domain of principal ideals. (English. Russian original) Zbl 1437.15022 J. Math. Sci., New York 243, No. 1, 45-55 (2019); translation from Mat. Metody Fiz.-Mekh. Polya 60, No. 2, 41-50 (2017). Reviewer: George Stoica (Saint John) MSC: 15A24 13F10 PDFBibTeX XMLCite \textit{V. M. Prokip}, J. Math. Sci., New York 243, No. 1, 45--55 (2019; Zbl 1437.15022); translation from Mat. Metody Fiz.-Mekh. Polya 60, No. 2, 41--50 (2017) Full Text: DOI
Clark, Pete L. Rabinowitsch times six. (English) Zbl 1455.11063 Rocky Mt. J. Math. 49, No. 2, 433-485 (2019). Reviewer: Meinhard Peters (Münster) MSC: 11E16 PDFBibTeX XMLCite \textit{P. L. Clark}, Rocky Mt. J. Math. 49, No. 2, 433--485 (2019; Zbl 1455.11063) Full Text: DOI Euclid Backlinks: MO
Conidis, Chris J.; Nielsen, Pace P.; Tombs, Vandy Transfinitely valued Euclidean domains have arbitrary indecomposable order type. (English) Zbl 1411.13030 Commun. Algebra 47, No. 3, 1105-1113 (2019). Reviewer: Moshe Roitman (Haifa) MSC: 13F07 13A05 13B25 13G05 PDFBibTeX XMLCite \textit{C. J. Conidis} et al., Commun. Algebra 47, No. 3, 1105--1113 (2019; Zbl 1411.13030) Full Text: DOI arXiv
Murty, M. Ram; Srinivas, Kotyada; Subramani, Muthukrishnan Admissible primes and Euclidean quadratic fields. (English) Zbl 1425.11168 J. Ramanujan Math. Soc. 33, No. 2, 135-147 (2018). MSC: 11R04 11A05 PDFBibTeX XMLCite \textit{M. R. Murty} et al., J. Ramanujan Math. Soc. 33, No. 2, 135--147 (2018; Zbl 1425.11168) Full Text: Link
Lemos, Abílio; de Oliveira, Pedro H. A. Suggested corrections for “A principal ideal domain that is not a Euclidean domain”. (English) Zbl 1429.13015 Am. Math. Mon. 125, No. 5, 425-425 (2018). MSC: 13F07 13F10 11R04 PDFBibTeX XMLCite \textit{A. Lemos} and \textit{P. H. A. de Oliveira}, Am. Math. Mon. 125, No. 5, 425--425 (2018; Zbl 1429.13015) Full Text: DOI
Chang, Wen-Yao; Cheng, Chih-Ren; Leu, Ming-Guang A remark on the ring of algebraic integers in \(\mathbb{Q}(\sqrt {- d})\). (English) Zbl 1365.11118 Isr. J. Math. 216, No. 2, 605-616 (2016). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R04 11R11 13F07 PDFBibTeX XMLCite \textit{W.-Y. Chang} et al., Isr. J. Math. 216, No. 2, 605--616 (2016; Zbl 1365.11118) Full Text: DOI
Long, D. D.; Thistlethwaite, Morwen B. Lenstra-Hurwitz cliques and the class number one problem. (English) Zbl 1406.11107 J. Number Theory 162, 564-577 (2016). MSC: 11R29 20H10 PDFBibTeX XMLCite \textit{D. D. Long} and \textit{M. B. Thistlethwaite}, J. Number Theory 162, 564--577 (2016; Zbl 1406.11107) Full Text: DOI
Clark, Pete L. A note on Euclidean order types. (English) Zbl 1315.13033 Order 32, No. 2, 157-178 (2015). MSC: 13F07 PDFBibTeX XMLCite \textit{P. L. Clark}, Order 32, No. 2, 157--178 (2015; Zbl 1315.13033) Full Text: DOI arXiv
Graves, Hester Growth results and Euclidean ideals. (English) Zbl 1290.11140 J. Number Theory 133, No. 8, 2756-2769 (2013). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11R04 13F07 11N36 PDFBibTeX XMLCite \textit{H. Graves}, J. Number Theory 133, No. 8, 2756--2769 (2013; Zbl 1290.11140) Full Text: DOI arXiv
Cerri, Jean-Paul; Chaubert, Jérôme; Lezowski, Pierre Euclidean totally definite quaternion fields over the rational field and over quadratic number fields. (English) Zbl 1280.11073 Int. J. Number Theory 9, No. 3, 653-673 (2013). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11R52 13F07 11R80 11Y40 PDFBibTeX XMLCite \textit{J.-P. Cerri} et al., Int. J. Number Theory 9, No. 3, 653--673 (2013; Zbl 1280.11073) Full Text: DOI
Chen, Ching-An; Leu, Ming-Guang On a proposition of Samuel and 2-stage Euclidean algorithm in global fields. (English) Zbl 1310.11105 J. Number Theory 133, No. 1, 215-225 (2013). MSC: 11R04 11A05 13F07 PDFBibTeX XMLCite \textit{C.-A. Chen} and \textit{M.-G. Leu}, J. Number Theory 133, No. 1, 215--225 (2013; Zbl 1310.11105) Full Text: DOI
Chen, Ching-An; Leu, Ming-Guang The 2-stage Euclidean algorithm and the restricted Nagata’s pairwise algorithm. (English) Zbl 1239.13028 J. Algebra 348, No. 1, 1-13 (2011). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 13F07 11R04 PDFBibTeX XMLCite \textit{C.-A. Chen} and \textit{M.-G. Leu}, J. Algebra 348, No. 1, 1--13 (2011; Zbl 1239.13028) Full Text: DOI
Bhaskara Rao, K. P. S. Products of idempotent matrices over integral domains. (English) Zbl 1165.15016 Linear Algebra Appl. 430, No. 10, 2690-2695 (2009). Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15B33 15A23 13F07 13F10 11A55 PDFBibTeX XMLCite \textit{K. P. S. Bhaskara Rao}, Linear Algebra Appl. 430, No. 10, 2690--2695 (2009; Zbl 1165.15016) Full Text: DOI
Leu, Ming-Guang The restricted Nagata’s pairwise algorithm and the Euclidean algorithm. (English) Zbl 1152.13016 Osaka J. Math. 45, No. 3, 807-818 (2008). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 13F07 11R04 PDFBibTeX XMLCite \textit{M.-G. Leu}, Osaka J. Math. 45, No. 3, 807--818 (2008; Zbl 1152.13016) Full Text: Euclid
Hebisch, Udo; Weinert, Hanns Joachim Left Euclidean \((2,2)\)-algebras. (English) Zbl 1130.16021 Commun. Algebra 35, No. 6, 2035-2055 (2007). Reviewer: Wen-Fong Ke (Tainan) MSC: 16Y99 16U30 16Y60 PDFBibTeX XMLCite \textit{U. Hebisch} and \textit{H. J. Weinert}, Commun. Algebra 35, No. 6, 2035--2055 (2007; Zbl 1130.16021) Full Text: DOI
Lankford, Dallas Generalized Gröbner bases: theory and applications. A condensation. (English) Zbl 1503.68128 Dershowitz, Nachum (ed.), Rewriting techniques and applications. 3rd international conference, RTA-89, Chapel Hill, NC, USA, April 3–5, 1989. Proceedings. Berlin etc.: Springer-Verlag. Lect. Notes Comput. Sci. 355, 203-221 (1989). MSC: 68Q42 03F65 13P10 PDFBibTeX XMLCite \textit{D. Lankford}, Lect. Notes Comput. Sci. 355, 203--221 (1989; Zbl 1503.68128) Full Text: DOI
Pan, Luquan On the D-bases of polynomial ideals over principal ideal domains. (English) Zbl 0668.68034 J. Symb. Comput. 7, No. 1, 55-69 (1989). Reviewer: D.Yu.Grigor’ev MSC: 68W30 13B25 13F07 13F10 13F15 PDFBibTeX XMLCite \textit{L. Pan}, J. Symb. Comput. 7, No. 1, 55--69 (1989; Zbl 0668.68034) Full Text: DOI
Schrieber, Leonard Recursive properties of Euclidean domains. (English) Zbl 0574.03029 Ann. Pure Appl. Logic 29, 59-77 (1985). Reviewer: P.Clote MSC: 03D45 03C57 03F65 PDFBibTeX XMLCite \textit{L. Schrieber}, Ann. Pure Appl. Logic 29, 59--77 (1985; Zbl 0574.03029) Full Text: DOI
Queen, Clifford Some arithmetic properties of subrings of function fields over finite fields. (English) Zbl 0303.12008 Arch. Math. 26, 51-56 (1975). MSC: 11R58 20G30 PDFBibTeX XMLCite \textit{C. Queen}, Arch. Math. 26, 51--56 (1975; Zbl 0303.12008) Full Text: DOI
Queen, Clifford Euclid’s algorithm in global fields. (English) Zbl 0289.12015 Bull. Am. Math. Soc. 79(1973), 1229-1232 (1974). MSC: 11R58 11R04 PDFBibTeX XMLCite \textit{C. Queen}, Bull. Am. Math. Soc. 79, 1229--1232 (1974; Zbl 0289.12015) Full Text: DOI
Samuel, Pierre About Euclidean rings. (English) Zbl 0223.13019 J. Algebra 19, 282-301 (1971). MSC: 13F07 PDFBibTeX XMLCite \textit{P. Samuel}, J. Algebra 19, 282--301 (1971; Zbl 0223.13019) Full Text: DOI
Gilmer, R.; Mott, J. Integrally closed subrings of an integral domain. (English) Zbl 0211.06502 Trans. Am. Math. Soc. 154, 239-250 (1971). MSC: 13B22 13G05 PDFBibTeX XMLCite \textit{R. Gilmer} and \textit{J. Mott}, Trans. Am. Math. Soc. 154, 239--250 (1971; Zbl 0211.06502) Full Text: DOI