An interview with Themba Andrew Dube (A TAD Interview)



Department of Mathematical Sciences, University of South Africa, P.O.Box 392, Tshwane, UNISA 0003, South Africa.\\ National Institute for Theoretical and Computational Sciences (NITheCS), Johannesburg, South Africa.



The paper covers an interview with Professor Themba Andrew Dube that captures his academic career that spans ordered algebraic structures, frames (locales), category theory, and pointfree function rings. The dialogue between the author and Dube features some of the work of Dube's doctoral students that influenced his research direction. The collaborative work of Dube and his relationships with prominent local and international scholars is exchanged in the conversation. We also narrate Dube's academic citizenry in Quaestiones Mathematicae, the journal of the South African Mathematical Society, whilst he was Editor-in-Chief. The paper gives a valuable historical account of Dube's contribution to the South African mathematical landscape and the African mathematical diaspora.


Main Subjects

[1] Baloolal, D., Some Topics in General Topology, DPhil, University of Oxford (1980).
[2] Dube, T., Structures in Frames, Ph.D. Thesis, University of Durban-Westville (1992).
[3] Dube, T., The Tamano-Dowker type theorems for nearness frames, J. Pure Appl. Algebra 99 (1995), l-7.
[4] Dube, T., Sigma-compactness via Nearness, Kyungpook Math. J. 39 (1999), 207-214.
[5] Dube, T., An algebraic view of weaker forms of realcompactness, Algebra Universalis 55 (2006), 187-202.
[6] Dube, T., Some ring-theoretic properties of almost P-frames, Algebra Universalis 60 (2009), 145-162.
[7] Dube, T., Concerning maximal l-ideals of rings of continuous integer-valued functions, Algebra Universalis 72 (2014), 359-370.
[8] Dube, T., A note on lattices of z-ideals of f-rings, N. Y. J. Math. 22 (2016), 351-361.
[9] Dube, T., Commutative rings in which zero-components of essential primes are essential, J. Algebra its Appl. 16 (2017), 17502024 (15 pages).
[10] Dube, T., On quasi-normality of function rings, Rocky Mt. J. Math. 40 (2018), 157-179.
[11] Dube, T., Rings in which sums of d-ideals are d-ideals, J. Korean Math. Soc. 56 (2019), 539-558.
[12] Dube, T., On the socle of an algebraic frame, Bulletin math´ematique de la Soci´et´e des Sciences Math´ematiques de Roumanie 62(110) No. 4 (2019), 371-385.
[13] Dube, T., First steps going down on algebraic frames, Hacet. J. Math. Stat. 48 (2019), 1792-1807.
[14] Dube, T., Notes on Pointfree Disconnectivity with a Ring-theoretic Slant, Appl. Categ. Struct. 18(1) (2010), 55-72.
[15] Dube, T., On the maximal regular ideal of pointfree function rings, and more, Topol. Appl. 273 (2020), 106960.
[16] Dube, T., Amenable and locally amenable algebraic frames, Order 37 (2020), 509-528.
[17] Dube, T. and Ighedo O., Comments regarding d-ideals of certain f-rings, J. Algebra its Appl. 12 (2013), 1350008 (16 pages).
[18] Dube, T. and Ighedo O., Two functors induced by certain ideals of function rings, Appl. Categ. Struct. 22 (2014), 663-681.
[19] Dube, T. and Ighedo O., On z-ideals of pointfree function rings, Bull. Iran. Math. Soc. 40 (2014), 657-675.
[20] Dube, T. and Ighedo O., More ring-theoretic characterizations of P-frames, J. Algebra its Appl. 14(5) (2015), 150061 (8 pages).
[21] Dube, T. and Ighedo O., Covering maximal ideals with minimal primes, Algebra Universalis 74 (2015), 411-424.
[22] Dube, T. and Ighedo O., Higher order z-ideals in commutative rings, Miskolc Math. Notes 17 (2016), 171-185.
[23] Dube, T. and Ighedo O., On lattices of z-ideals of function rings, Mathematica Slovaca 68 (2018), 271-284.
[24] Dube, T. and Ighedo O., Concerning the summand intersection property in function rings, Houst. J. Math. 44 (2018), 1029-1049.
[25] Dube, T. and Naidoo, I., On openness and surjectivity of lifted frame homomorphisms, Topol. Appl. 157 (2010), 2159-2171.
[26] Dube, T. and Naidoo, I., Erratum to “On openness and surjectivity of lifted frame homomorphisms”, Topol. Appl. 157 (2011), 2257-2259.
[27] Dube, T. and Naidoo, I., When lifted frame homomorphisms are closed, Topol. Appl. 159 (2012), 3049-3058.
[28] Dube, T. and Naidoo, I., Round squares in the category of Frames, Houst. J. Math. 39(2) (2013), 453-473.
[29] Dube, T. and Nsonde Nsayi, J., When rings of continuous functions are weakly regular, Bull. Belg. Math. Soc. Simon Stevin 22 (2015), 213-226.
[30] Dube, T. and Nsonde Nsayi, J., When certain prime ideals in rings of continuous functions are minimal or maximal, Topol. Appl. 192 (2015), 98-112.
[31] Dube, T. and Nsonde Nsayi, J., Another ring-theoretic characterization of boundary spaces, Houst. J. Math. 42 (2016), 709-722.
[32] Dube, T. and Sithole, S., On the sublocale of an algebraic frame induced by the d-nucleus, Topol. Appl. 263 (2019), 90-106.
[33] Dube, T. and Stephen, D.N., On ideals of rings of continuous functions associated with sublocales, Topol. Appl. 284 (2020), 107360.
[34] Dube, T. and Stephen, D.N., Mapping Ideals to Sublocales, Appl. Categ. Struct. 29 (2021), 747-772.
[35] Dube, T. and Walters-Wayland, J., Coz-onto Frame Maps and Some Applications, Appl. Categ. Struct. 15 (2007), 119-133.
[36] Ighedo, O., Concerning ideals of pointfree function rings, Ph.D. Thesis, University of South Africa (2013).
[37] Ighedo, O., More on the functor induced by z-ideals, Appl. Categ. Struct. 26 (2018), 459-476.
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[39] Matlabyana, M.Z., Coz-related and other special quotients in frames, Ph.D. Thesis, University of South Africa (2012).
[40] Mugochi, M.M., Contributions to the theory of nearness in pointfree topology, Ph.D. Thesis, University of South Africa (2009).
[41] Ngo Babem, A.F., On localic convergence with applications, Master’s dissertation, University of South Africa (2019).
[42] Nsonde Nsayi, J,, Variants of P-frames and associated rings, Ph.D. Thesis, University of South Africa (2015).
[43] Nongxa, L.G., A problem in abelian group theory, DPhil, University of Oxford (1982).
[44] Ori, R.G., Smallest and Largest Members of Certain Classes of F-Proximities, Ph.D. Thesis, University of Colorado at Boulder (1975).
[45] Pretorius, J.P.G., On the Structure of (Free) Heyting Algebras, Ph.D. thesis, University of Cambridge (1993).
[46] Stephen, D.N., Ideals of function rings associated with sublocales, Ph.D. Thesis, University of South Africa (2021).