Futa, Yuichi; Shidama, Yasunari Dual lattice of \(\mathbb{Z}\)-module lattice. (English) Zbl 1377.06009 Formaliz. Math. 25, No. 2, 157-169 (2017). MSC: 06F10 06D50 13A99 03B35 PDFBibTeX XMLCite \textit{Y. Futa} and \textit{Y. Shidama}, Formaliz. Math. 25, No. 2, 157--169 (2017; Zbl 1377.06009) Full Text: DOI
Futa, Yuichi; Shidama, Yasunari Embedded lattice and properties of Gram matrix. (English) Zbl 1365.13015 Formaliz. Math. 25, No. 1, 73-86 (2017). MSC: 13C10 15A09 15A63 03B35 PDFBibTeX XMLCite \textit{Y. Futa} and \textit{Y. Shidama}, Formaliz. Math. 25, No. 1, 73--86 (2017; Zbl 1365.13015) Full Text: DOI
Futa, Yuichi; Shidama, Yasunari Lattice of \(\mathbb{Z}\)-module. (English) Zbl 1343.13017 Formaliz. Math. 24, No. 1, 49-68 (2016). MSC: 13C99 15A63 03B35 PDFBibTeX XMLCite \textit{Y. Futa} and \textit{Y. Shidama}, Formaliz. Math. 24, No. 1, 49--68 (2016; Zbl 1343.13017) Full Text: DOI
Futa, Yuichi; Shidama, Yasunari Divisible \(\mathbb{Z}\)-modules. (English) Zbl 1343.13014 Formaliz. Math. 24, No. 1, 37-47 (2016). MSC: 13C13 13C05 15A03 03B35 PDFBibTeX XMLCite \textit{Y. Futa} and \textit{Y. Shidama}, Formaliz. Math. 24, No. 1, 37--47 (2016; Zbl 1343.13014) Full Text: DOI
Futa, Yuichi; Okazaki, Hiroyuki; Shidama, Yasunari Torsion part of \(\mathbb{Z}\)-module. (English) Zbl 1334.13008 Formaliz. Math. 23, No. 4, 297-307 (2015). MSC: 13C12 13C10 03B35 PDFBibTeX XMLCite \textit{Y. Futa} et al., Formaliz. Math. 23, No. 4, 297--307 (2015; Zbl 1334.13008) Full Text: DOI
Futa, Yuichi; Okazaki, Hiroyuki; Shidama, Yasunari Matrix of \(\mathbb{Z}\)-module. (English) Zbl 1317.11037 Formaliz. Math. 23, No. 1, 29-49 (2015). MSC: 11E39 13C10 03B35 PDFBibTeX XMLCite \textit{Y. Futa} et al., Formaliz. Math. 23, No. 1, 29--49 (2015; Zbl 1317.11037) Full Text: DOI
Futa, Yuichi; Okazaki, Hiroyuki; Nakasho, Kazuhisa; Shidama, Yasunari Torsion \(\mathbb Z\)-module and torsion-free \(\mathbb Z\)-module. (English) Zbl 1316.13012 Formaliz. Math. 22, No. 4, 277-289 (2014). MSC: 13C10 13C12 03B35 PDFBibTeX XMLCite \textit{Y. Futa} et al., Formaliz. Math. 22, No. 4, 277--289 (2014; Zbl 1316.13012) Full Text: DOI
Nakasho, Kazuhisa; Futa, Yuichi; Okazaki, Hiroyuki; Shidama, Yasunari Rank of submodule, linear transformations and linearly independent subsets of \(\mathbb Z\)-module. (English) Zbl 1311.13009 Formaliz. Math. 22, No. 3, 189-198 (2014). MSC: 13C10 03B35 PDFBibTeX XMLCite \textit{K. Nakasho} et al., Formaliz. Math. 22, No. 3, 189--198 (2014; Zbl 1311.13009) Full Text: DOI
Futa, Yuichi; Okazaki, Hiroyuki; Shidama, Yasunari Submodule of free \(\mathbb Z\)-module. (English) Zbl 1298.13013 Formaliz. Math. 21, No. 4, 273-282 (2013). MSC: 13C10 03B35 PDFBibTeX XMLCite \textit{Y. Futa} et al., Formaliz. Math. 21, No. 4, 273--282 (2013; Zbl 1298.13013) Full Text: DOI