E. FRANK CORNELIUS, PhD, JD

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2.  A generalization of separable groups, Pacific J Math, 39, no. 3 (1970), 603-613 

Citations:

(a)  Benabdallah, K., Groupes Abeliens Sans-Torsion (Univ of Montreal Press 1981), @ 67 & 68 

(b)  Mishina, A. P., Abelian groups, J Math Sci (New York), 18, no. 5 (1982), 629-668, @ 635, 637 & 659 

(c)  Macias-Diaz, J., A generalization of the Pontryagin-Hill theorems to projective modules over Prufer domains, Pacific J Math, 246, no. 2 (2010), 391-405, @ 392 & 404 

(d)  Macias-Diaz, J. E., On the unions of ascending chains of direct sums of ideals of h-local Prufer domains, Algebra Colloquium, 18, no. spec01 (2011), 749-757, @ 750 & 757 

(e)  Braun, G.; Schultz, P.; Strungmann, L., Decompositions of torsion-free abelian groups, J Algebra, 528 (June 2019), 72-84; Preprint 2018, @ 3 & 12. 

 

3.  Characterization of a class of torsion free groups in terms of endomorphisms, Pacific J Math, 70, no. 2 (1978), 341-355; submission date corrected to February 5, 1974, Pacific J Math, 85, no. 2 (1979), 501

Citations:

(a)  Benabdallah, K., Groupes Abeliens Sans-Torsion (Univ. of Montreal Press 1981) @ 55, 65, 67 & 68 

(b)  Markov, T.; Mikhalev, V.; Skornyakov, L. A.; Tuganbaev, A. A., Endomorphism rings of modules and lattices of submodules, J Math Sci (NY), 31, no. 3 (1985), 3005—3051, @ 3008 & 3037 

(c)  Mishina, A. P., Abelian groups, J Math Sci, 40, no. 3 (1988), 288-330, @ 297 & 323 

(d)  Krylov, P. A.; Mikhalev, A. V.; Tuganbaev, A. A., Endomorphism rings of abelian groups, J Math Sci, 110, no. 3 (NY 2002), 2683-2745, @ 2733 

(e)  Krylov, P. A.; Mikhalev, A. V.; Tuganbaev, A. A., Properties of endomorphism rings of abelian groups, I, J Math Sci (NY), 112, no. 6 (2002), 4598—4735, @ 4721 

(f)  Krylov, P. A.; Mikhalev, A. V.; Tuganbaev, A. A., Properties of endomorphism rings of abelian groups, II, J Math Sci. (NY) 113, no. 1 (2003), 1—174, @ 159 

(g)  Krylov, P. A.; Mikhalev, A. V.; Tuganbaev, A. A., Endomorphism Rings of Abelian Groups (Kluwer Academic Publications 2003) @ 418.

 

4.  A sufficient condition for separability, J Algebra, 67, no. 2 (1980), 476-478 

Citations:

(a)  Metelli, C., On type-related properties of torsionfree abelian groups, in Abelian Group Theory, Gobel, R.; Lady, L.; Mader, A., eds., vol. 1006, Lecture Notes in Mathematics (Springer-Verlag 1983) 253-267, @ 266 & 267 

(b)  Fuchs, L.; Viljoen, G., A generalization of separable torsion-free abelian groups, Rend Sem Mat Univ Padova, 73 (1985), 15-21, @ 15 & 21 

(c)  Rangaswamy, K. M., On C-separable abelian groups, Commun Algebra, 13, no. 6 (1985), 1219-1227, @ 1219, 1220, 1223 & 1226 

(d)  Mishina, A. P., Abelian groups, J Math Sci, 40, no. 3 (1988), 288-330, @ 293 & 323 

(e)  Albrecht, A.; Hill, P., Separable Vector Groups, in Fuchs, L.; Gobel, R.; Schultz, P., eds., vol. 87, Contemporary Mathematics, (AMS 1989), 155-160, @ 158 & 160 

(f)  Dugas, M.; Oxford, E. P., Preradicals induced by torsion free abelian groups, Commun Algebra, 17, no. 4 (1989) 

(g)  Grinshpon, S. Ya, Quite characteristic subgroups of separable abelian groups, Foundation and adj Mat, 4, no. 4 (1998), 1279-1305 

(h)  Van Oystaeyen, F., Separable algebras, in Handbook of Algebra, vol. 2, Hazenwinkel, M., ed., (North Holland 2000) 461-505, @ 490 

(i)  Grinshpon, S. Ya.; Krylov, P. A., Fully invariant subgroups, full transitivity, and homomorphism groups of abelian groups, J Math Sci (NY) 128, no. 3 (2005) 2894—2997, @ 2960 & 2995 

(j)  Fuchs, L., Abelian Groups (Springer Switzerland 2015) @ 507

    

5.  Cardinalities of chains of sets, Abstracts Amer Math Soc, 2 (1981) 486

 

6.  Polynomial points (with P. Schultz), J Integer Sequences, 10 (2007), article 07.3.6

Citation:

(a)  N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, sequence A000178/ M2049

 

7.  Product bases and endomorphisms of products of integers, 16 pages. Product Bases 

 

8.  Sequences generated by polynomials (with P. Schultz), Amer Math Monthly, 115, no. 2 (2008), 154-158 

Citations:

(a)  N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, sequences A135049, A135185, A135256, A136456, A136457 & A137296

(b)  Kim, V.; Laohakosol, V.; Prugsapitak, S., Sequences generated by polynomials over integral domains, Walailak J Sci Tech, 16, no. 9 (2019), 625-633, @ 625, 630 & 633 

(c)  Kim, V.; Laohakosol, V.; Prugsapik, S., Differential and difference polynomial sequences, Notes on Number Theory and Discrete Mathematics, 25, no. 4 (2019) 

 

9.  Multinomial points (with P. Schultz), Houston J Math, 34, no. 3 (2008), 661-676

Citation:
(a) Ikenmeyer, C.; Pak, I., What is in #P and what is not?, 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), Denver, CO (2022) 860-871, https://arxiv.org/pdf/2204.13149.pdf, @ 77

 

10.  Root bases of polynomials over integral domains (with P. Schultz), in Models, Modules and Abelian Groups, R. Gobel & B. Goldsmith, eds., (Walter de Gruyter Berlin 2008), 237-250

Citation:

(a)  Schultz, P., Bases for direct products, in Algebras, Representations and Applications, Futorny, V.; Kac, V.; Kashuba, I. and Zelmanov, E., eds., Contemporary Mathematics, Amer Math Soc 483 (2009) 253-259, @ 254, 257 & 258

 

11.  Identities for complete homogeneous symmetric polynomials, JP J Algebra, Number Theory & Applications, 21, no. 1 (2011), 109-116

Citations:

(a)  Stawiska, M., Liouville theorem with parameters; asymptotics of certain rational integrals in differential fields, Annales Societatis Mathematicae Polonae, Series I, Commentationes Mathematicae, 50, no. 2 (2010) 155-159, @ 157 & 159

(b)  Toth, L., Two generalizations of the Busche-Ramanujan identities, Int'l J Number Theory, 9, no. 5 (2013) 1301-1311, @ 1304 & 1310

(c)  Fullwood, J.; Helmer, M., On a Projective Bundle Formula, Projective Bundle, 2016, @ 8, 11, 14, 16  

(d)  Bekker, B.M.; Ivanov, O.A.; Merkurjev, A.S., An algebraic identity and the Jacobi-Trudi formula, Vestnik S. Petersburg University; Mathematics, 49, no. 1 (2016) 1-4, @ 4 

(e)  Deng, X.; Lopez-Martinez, C., On the Use of the 12-Norm for Texture Analysis of Polarimetric SAR Data, IEEE Transactions on Geoscience and Remote Sensing, 54, no. 11 (Nov 2016) 6385 - 6398, @ 6388

(f)  Esole, M.; Jefferson, P.; and Kang, M. J., Euler Characteristics of Crepant Resolutions of Weierstrass Models, Commun Math Phys, 371, no. 1 (October 2019), 99-144; Crepant Resolutions, @ 32, 41 

(g)  Toth, L., Asymptotic Properties of Multiplicative Arithmetic Functions of One and Several Variables, Asymptotic Properties, 2018, @ 111, 117 

(h)  Adams, S.; Vogel, Q., Space-Time Random Walk Loop Measures, Space-Time, May 2018, @ 28, 34

(i)  Kang, K., Two Views on Gravity: F-Theory and Holography, Gravity, April 2019, @ 247, 892

(j)  Yamaleev, R. M., Divided Differences Calculus in Matrix Representations, Int'l J Appl and Comput Math, 132, no. 5 (October 2019), reference 9

(k)  Basak, A.; Vogel, M; Zeitouni, O., Localization of eigenvectors of non-Hermitian banded noisy Toeplitz matrices, Localization, March 31, 2021, @ 34, 97

(l)  Jeong, Haewon; Devulapalli, Ateet; Cadambe, Viveck R.; Calmon, Flavio, ε-Approximate Coded Matrix Multiplication is Nearly Twice as Efficient as Exact Multiplication, Coded Matrix, May 5, 2021, @ 19, 26

(m) Oliveira, D.; Martínez, F.E.B., Artin-Schreier curves given by Fq-linearized polynomials, Discrete Mathematics, 346, No. 12, December 2023, @ Theorem 2.5, Article Preview

 

12.  Endomorphisms and product bases of the Baer-Specker group, Int'l J Math and Math Sciences, 2009, article 396475

 

13.  Properties of slender rings, Int'l J Math and Math Sciences, 2010, article 162464

 

14. Generic combinatorial identities, JP J Algebra, Number Theory and Applications, 31, No. 1 (2013) 1-4

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15. 1-separable torsion free modules over integral domains, JP J Algebra, Number Theory and Applications, 59 (2022), 1-16
http://dx.doi.org/10.17654/0972555522035

 

16. Miscellaneous citations to Frank Cornelius:

(a) Weiss, M. D., Algebraic and other entropies of group endomorphisms, Mathematical Systems Theory, 8, no. 3 (1975), 243-248, @ 248

 

Frank Cornelius has lectured on his research results before the Seminaire de Mathematiques Superieures at the University of Montreal (1979); before the 789th Meeting of the American Mathematical Society at the University of Massachusetts in Amherst (1981); before the 1st Joint Meeting of the American Mathematical Society and the New Zealand Mathematical Society (2007); at the 2019 Spring Meeting, Michigan Section, Mathematical Association of America; and at departmental colloquia.

He has served as an Adjunct Professor of Mathematics at the University of Detroit Mercy. He previously taught mathematics and computer programming at the University of Washington and Wayne State University. He is a member of the Mathematical Association of America.