User:Shivdattk/sandbox

Shiv Datt Kumar (born 1965) is an Indian Mathematician and Professor at Motilal Nehru National Institute of Technology  Allahabad Prayagraj, India. He is also a very good academic administrator. His main research area is Commutative Algebra. He is an versatile Mathematician. He has worked in several other areas like number theory, Hopf Algebra, Fuzzy Theory, Algebraic Differential equations etc. He is an excellent teacher and has got best Teacher Award 2004 and best Professor of Mathematics Dewang Mehta National Educations Award in 1917. He got VDGOOD International Scientists Awards in the category of Engineering, Sciences & Medicine in 2020.

He was born on 10 August 1965 in village- Reewan, District- Hamirpur (UP). His father Late Shiv Mohan Tripathi was a farmer, and Mother Savitri Tripathi, a homemaker. After completing his schooling from  Junior High School Reewan, Hamirpur(UP), Govt Inter College Hamirpur (UP) he earned his Bachelor of Arts degree in 1986 and his Master’s degree (MA) in 1988 from the from the  University of Allahabad, Prayagaraj. He did his doctoral work in Commutative Algebra in Harish-Chandra Research Institute Allahabad.

Shiv Datt Kumar has made a number of major original contributions to the subject of Commutative Algebra, including his landmark papers (i) on Involutivity of the Characteristic Variety (ii) Rees algebra over an ideal in t-rings, with his student Jyoti Singh. His other remarkable are work with Mamta Balodi and Hua-Lin Huang (i)  On the classification of finite quasi-quantum groups  (ii) Finite Majid algebras over the Klein’s group.

References:


 * 1) ( Ajim ANSARI, Brajesh SHARMA, Shiv Datt Kumar, Srinivas BEHARA), Graded Prime Ideals Attached to a Group Graded Module, Iranian Journal of Mathematical Sciences and Informatics, 2021 (accepted).
 * 2) (Srinivasarao Thota, Shiv Datt Kumar), A new reduction algorithm for differential-algebraic systems with power series coefficients, Information Sciences Letters, 2021, Vol 10(1), 59-66.
 * 3) (Srinivasarao Thota, Shiv Datt Kumar), Symbolic Algorithm to Solve Initial Value Problems for Partial Differential Equations, Bulletin of Computational Applied Mathematics, Vol 8, Issue 1, 2020,
 * 4) ( Ajim Uddin Ansari, B. K. Sharma, Shiv Datt Kumar), Different Types of G-Prime Ideals Associated to a Graded Module and Graded Primary Decomposition in a graded Prufer Domain, International Electronic Journal of Algebra, (Scopus Indexed), Vol 28, Issue 28, Pages 141 - 155, 2020, https://doi.org/10.24330/ieja.768206
 * 5) (Abhishek Juyal, Shiv Datt Kumar), On the family of elliptic curves y2 = x3 − m2x + p2, Proceedings- Mathematical Sciences, (Indian Academy of Sciences) (Springer Publication-SCI Journal), Vol 128 (5), 2018, page 54-,ISSN: 0253-4142. E-ISSN: 0973-7685. doi.org/10.1007/s12044 − 018 − 0433−0
 * 6) (Kalyan Chakraborty; Abhishek Juyal; Shiv Datt Kumar; Bibekananda Maji), An asymptotic expansion of a Lambert series associated to cusp forms. Int. J. Number Theory SCI Journal, Vol 14 (2018), no. 1, 289-299, MR3726254
 * 7) (Mamta Balodi, Hua-Lin Huang, Shiv Datt Kumar), On the classification of finite quasi-quantum groups Re- views in Mathematical Physics, SCI Indexed, World Scientific Publication, Vol 29, No.10, 2017, pages 11730003-22, PISSN:0129-055X E-ISSN:1793-6659, DOI: 10.1142/S0129055X17300035, MR3720509
 * 8) (Sumit Kumar Upadhyay, Shiv Datt Kumar, Raja Sridharan) “Projective modules and efficient generation of ideals over Laurent polynomial rings”, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, Vol 87(3), 349-453, 2017 (Springer Publication) SCI Journal, In press. ISSN: 0369-8203, E-ISSN: 2250-1762. Impact factor 0.390, DOI : 10.1007/s40010 − 017 − 0381 − 6, MR3680003
 * 9) (Jyoti Singh, Shiv Datt Kumar) “Mathematical Counterpart of the Heisenberg Uncertainty Principle” for publication in the Reports on Mathematical Physics, (Elsevier Publication, Scopus Journal, Vol 80 (2), 2017, 161-176, ISSN: 0034-4877, DOI : 10.1016/S0034−4877(17)30074−5, MR3721904 Impact factor 0.870.
 * 10) ( Sumit Kumar Upadhyay, Shiv Datt Kumar, Raja Sridharan) Connection between commutative algebra and topology, Indian Journal of Pure and Applied Mathematics (Springer Publication), SCI Journal, Vol 47 (3), 471-489, September, 2016, Indian National Science Academy Publi- cation, DOI : 10.1007/s13226 − 016 − 0179 − 2, P ISSN: 0019-5588, E ISSN: 0975-7465.
 * 11) (Mamta Balodi & Hua-Lin Huang, Shiv Datt Kumar) Diamond lemma for the group graded quasi-algebras, Proceedings Mathematical Sciences (Indian Academy of Sciences) (Springer Publica- tion), SCI Journal, Vol 126, Issue 3, pp 341-352, August 2016, DOI 10.1007/s12044-016-0292- 5. ISSN: 0253-4142, E ISSN: 0973-7685.
 * 12) (Srinivasarao Thota, Shiv Datt Kumar) Symbolic algorithm for a system of differential-algebraic equations, Kyungpook Mathematical Journal (Indexed: Scoupus, Korean SCI), 56(4), 2016, 1141-1160.
 * 13) (Srinivasarao Thota, Shiv Datt Kumar) Solving system of higher-order linear differential equations on the level of operators, International Journal of Pure and Applied Mathematics (Scopus Journal), Vol 106 (1), 2016, 11-21, ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version), doi: 10.12732/ijpam.v106i1.2.
 * 14) ( Jyoti Singh, Shiv Datt Kumar) Rees algebra over an ideal in t-rings, Journal of Pure and Applied Algebra, Elsevier Publication, SCI Journal, Volume 219, Issue 4, April 2015, Pages 830- 838, DOI : 10.1016/j.jpaa.2014.04.032, ISSN: 0022-4049, E ISSN: 1873-1376.
 * 15) (Priti Singh, Shiv Datt Kumar) Existence of reduction of ideals over semi local rings, The Mathematics Student, Vol 84, (No. 1- 2), 2015, IMS publication (Scopus Indexed).
 * 16) (Priti Singh, Shiv Datt Kumar) Reductions in Rees algebra of modules, Algebras and Representation Theory, Volume 17, No. 2, April, 2014, 17851795, Springer Publication, SCI Journal, DOI10.1007/s10468 − 014 − 9471 − 1. ISSN:1386-923X
 * 17) ( Mamta Balodi & Hua-Lin Huang, Shiv Datt Kumar) Finite Majid algebras over the Klein group, Commu- nications in Algebra, Taylor and Francis Publication, SCI Journal, Vol 42, Issue 11 (2014), pages 4962-4983 (ID: 828739 DOI:10.1080/00927872.2013.828739). ISSN: 0092-7872, E ISSN: 1532-4125.
 * 18) Jyoti Singh, Shiv Datt Kumar, On the Involutivity of the Characteristic Variety, Communications in Algebra, Taylor and Francis Publication, SCI Journal, 42, Issue 8 (2014), 3607-3618. (ID: 790393 DOI:10.1080/00927872.2013.790393). ISSN- 0092-7872, E ISSN- 1532-4125.
 * 19) (Shiv Datt Kumar, Raja Sridharan and Ratnesh Kumar Mishra Completion of unimodular row to an invertible matrix, Mitteilungen Klosterneuburg Journal, 64 (3) 2014, Scopus Journal. ISSN: 0007-5922
 * 20) (Sumit Kumar Upadhyay and Raja Sridharan, Shiv Datt Kumar) On the number of generators of a projec- tive module, Proceedings of the Indian Academy of Sciences-Mathematical Sciences, (Springer Publication), SCI Journal, Vol. 123, No. 4, November 2013, 469 - 478. DOI 10.1007/s12044- 013-0147-2. ISSN: 0253-4142, E ISSN: 0973-7685.
 * 21) Shiv Datt Kumar, Ratnesh Kumar Mishra,  Lifting of generators of ideals to Laurent polynomial ring, Beitrage zur Algebra und Geometrie (Contributions to Algebra and Geometry) (Scopus in- dexed) (Springer Publication), March 2013, Volume 54, Issue 1, pages 147-153, ISSN 0138- 4821. DOI: 10.1007/s13366-012-0102-x.
 * 22) Sumit Kumar Upadhyay, Shiv Datt Kumar, Existence of a unique group of finite order, the Mathematics Student, Vol 81, Nos. 1-4, December, 2012, pages 215-218 (ISSN: 0025-5742), IMS publication (Scopus Indexed).
 * 23) Srinivas Behara, Shiv Datt Kumar, Group graded associated ideals with flat base change of rings and short exact sequences, Proceedings of the Indian Academy of Sciences-Mathematical Sci- ences, (Springer Publication), SCI Journal, Vol. 121, No. 2, February 2011, 111–120. ISSN: 0253-4142, E ISSN: 0973-7685.
 * 24) Srinivas Behara,  Uniqueness of graded primary decomposition of modules graded over finitely generated Abelian groups, Communications in Algebra, Taylor and Francis Pub- lication, SCI Journal, Vol 39 (7), 2011, 2607-2614. ISSN- 0092-7872, E ISSN- 1532-4125.
 * 25) Markus Perling, Shiv Datt Kumar, Primary decomposition over rings graded by finite Abelian groups, Jour- nal of Algebra, Elsevier Publication, SCI Journal, 318(2), 2007, 553-561. ISSN: 0021-8693, E ISSN: 1090-266X.
 * 26) Shiv Datt Kumar, Sections of zero dimensional ideals over a Noetherian ring, Archiv der Mathematik, Birkhauser Verlag Basel, Switzerland Publication, SCI Journal, 89, 2007, 124-130. ISSN: 0003-889X, E ISSN: 1420-8938.
 * 27) (M. Tripathi and K. Pandey, Shiv Datt Kumar), Surface modification of Semiconductor Photo-electrode for improved Solar Cell performance, Solar Energy Materials and Solar Cells, Elsevier Pub- lication, SCI Journal, Volume 91, Issue 18, 2007, 1663-1668.
 * 28) Shiv Datt Kumar, A note on a graded ring analogue of Quillen’s theorem, Expositiones Mathematicae, Elsevier Publication, SCI Journal, Vol 22, 2004, 29-30. ISSN: 0723-0869, E ISSN: 1878-0792
 * 29) Shiv Datt Kumar, Ramji Lal Lifting of generators of an ideal and Nori’s Homotopy Conjecture, Indian Journal of Pure and Applied Mathematics (Springer Publication), SCI Journal, Indian National Science Academy Publication, Vol 34 (11), 2003, 1599-1610. ISSN: 0019-5588 (print version) ISSN: 0975-7465 (electronic version)
 * 30) Shiv Datt Kumar, Satya Mandal, Some results on generators of an ideal, Journal of Pure and Applied Algebra, Elsevier Publication, SCI Journal, Vol. 169 (1), 2002, 29-32. ISSN- 0022-4049, E ISSN 1873-1376.