Themba Dube
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Themba Dube has a total of 47 co-authors. Here are the top co-authors by number of shared publications:
- Inderasan Naidoo
Department of Mathematical Sciences, University of South Africa, Pretoria, South Africa
6 shared publications - Oghenetega Ighedo
Department of Mathematical Sciences, University of South Africa, Pretoria, South Africa
6 shared publications - Amartya Goswami
Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, South Africa
5 shared publications - Dimitrios N. Georgiou
Department of Mathematics, University of Patras, 26504 Patra, Greece
3 shared publications - Ali Akbar Estaji
Faculty of Mathematics and Computer science, Hakim Sabzevari University, Sabzevar, Iran
2 shared publications - Dorca Nyamusi Stephen
Department of Mathematical Sciences, University of South Africa, Pretoria, South Africa
2 shared publications
Latest Publications
- Open Access
- 14 January 2025
- Published by The International Electronic Journal of Algebra in International Electronic Journal of Algebra
- Vol. 37 (37) , 201-219
Revisiting Baer elements
The objective of this paper is to extend certain properties observed in $d$-ideals of rings and $d$-elements of frames to Baer elements in multiplicative lattices. Additionally, we present results concerning these elements that have not been addressed in the study of $d$-ideals of rings. Furthermore, we introduce Baer closures and explore Baer maximal, prime, semiprime and meet-irreducible elements.
- 14 January 2025
- Published by The International Electronic Journal of Algebra in International Electronic Journal of Algebra
- Vol. 37 (37) , 201-219
Open AccessRevisiting Baer elements
The objective of this paper is to extend certain properties observed in $d$-ideals of rings and $d$-elements of frames to Baer elements in multiplicative lattices. Additionally, we present results concerning these elements that have not been addressed in the study of $d$-ideals of rings. Furthermore, we introduce Baer closures and explore Baer maximal, prime, semiprime and meet-irreducible elements.
- Open Access
- 28 December 2024
- Published by Springer Nature in Algebra universalis
- Vol. 86 (1) , 1-23
On z-elements of multiplicative lattices
The aim of this paper is to investigate further properties of z-elements in multiplicative lattices. We utilize z-closure operators to extend several properties of z-ideals to z-elements and introduce various distinguished subclasses of z-elements, such as z-prime, z-semiprime, z-primary, z-irreducible, and z-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where z-elements are closed under finite products and a representation of z-elements in terms of z-irreducible elements in z-Noetherian multiplicative lattices.
- 28 December 2024
- Published by Springer Nature in Algebra universalis
- Vol. 86 (1) , 1-23
Open AccessOn z-elements of multiplicative lattices
The aim of this paper is to investigate further properties of z-elements in multiplicative lattices. We utilize z-closure operators to extend several properties of z-ideals to z-elements and introduce various distinguished subclasses of z-elements, such as z-prime, z-semiprime, z-primary, z-irreducible, and z-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where z-elements are closed under finite products and a representation of z-elements in terms of z-irreducible elements in z-Noetherian multiplicative lattices.
- Open Access
- 15 July 2024
- Published by Springer Nature in Rendiconti del Circolo Matematico di Palermo Series 2
- Vol. 73 (8) , 3105-3117
Some aspects of k-ideals of semirings
The aim of this paper is to study some distinguished classes of k-ideals of semirings, which include k-prime, k-semiprime, k-radical, k-irreducible, and k-strongly irreducible ideals. We discuss some of the properties of k-ideals and their products, intersections, and ideal quotients under semiring homomorphisms.
- 15 July 2024
- Published by Springer Nature in Rendiconti del Circolo Matematico di Palermo Series 2
- Vol. 73 (8) , 3105-3117
Open AccessSome aspects of k-ideals of semirings
The aim of this paper is to study some distinguished classes of k-ideals of semirings, which include k-prime, k-semiprime, k-radical, k-irreducible, and k-strongly irreducible ideals. We discuss some of the properties of k-ideals and their products, intersections, and ideal quotients under semiring homomorphisms.
- Open Access
On $z$-elements of multiplicative lattices
The aim of this paper is to investigate further properties of $z$-elements in multiplicative lattices. We utilize $z$-closure operators to extend several properties of $z$-ideals to $z$-elements and introduce various distinguished subclasses of $z$-elements, such as $z$-prime, $z$-semiprime, $z$-primary, $z$-irreducible, and $z$-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where $z$-elements are closed under finite products and a representation of $z$-elements in terms of $z$-irreducible elements in $z$-Noetherian multiplicative lattices.
Open AccessOn $z$-elements of multiplicative lattices
The aim of this paper is to investigate further properties of $z$-elements in multiplicative lattices. We utilize $z$-closure operators to extend several properties of $z$-ideals to $z$-elements and introduce various distinguished subclasses of $z$-elements, such as $z$-prime, $z$-semiprime, $z$-primary, $z$-irreducible, and $z$-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where $z$-elements are closed under finite products and a representation of $z$-elements in terms of $z$-irreducible elements in $z$-Noetherian multiplicative lattices.
- 21 December 2023
- Published by Elsevier in Topology and its Applications
- Vol. 344
Zip rings (resp. czip rings) and some applications
- 21 December 2023
- Published by Elsevier in Topology and its Applications
- Vol. 344
Zip rings (resp. czip rings) and some applications
- Open Access
Some aspects of $k$-ideals of semirings
The aim of this paper is to study some distinguished classes of $k$-ideals of semirings, which include $k$-prime, $k$-semiprime, $k$-radical, $k$-irreducible, and $k$-strongly irreducible ideals. We discuss some of the properties of $k$-ideals and their products, intersections, and ideal quotients under semiring homomorphisms.
Open AccessSome aspects of $k$-ideals of semirings
The aim of this paper is to study some distinguished classes of $k$-ideals of semirings, which include $k$-prime, $k$-semiprime, $k$-radical, $k$-irreducible, and $k$-strongly irreducible ideals. We discuss some of the properties of $k$-ideals and their products, intersections, and ideal quotients under semiring homomorphisms.
- Open Access
- 1 February 2023
- Published by CMV Verlag in Categories and General Algebraic Structures with Applications
- Vol. 18 (1)
Cover for Vol. 18, No. 1.
- 1 February 2023
- Published by CMV Verlag in Categories and General Algebraic Structures with Applications
- Vol. 18 (1)
Open AccessCover for Vol. 18, No. 1.
- 3 December 2022
- Published by Springer Nature in Algebra universalis
- Vol. 84 (1) , 1-28
Algebraic frames in which dense elements are above dense compact elements
- 3 December 2022
- Published by Springer Nature in Algebra universalis
- Vol. 84 (1) , 1-28
Algebraic frames in which dense elements are above dense compact elements
- 1 December 2022
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 72 (6) , 1429-1446
Ideals of functions with compact support in the integer-valued case
For a zero-dimensional Hausdorff space X, denote, as usual, by C(X, ℤ) the ring of continuous integer-valued functions on X. If f ∈ C(X, ℤ), denote by Z(f) the set of all points of X that are mapped to 0 by f. The set is the integer-valued analogue of the ideal of functions with compact support in C(X). By first working in the category of locales and then interpreting the results in spaces, we characterize this ideal in several ways. Writing ζ X for the Banaschewski compactification of X, we also explore some properties of ideals of C(X, ℤ) associated with subspaces of ζ X analogously to how one associates, for any Tychonoff space Y, subsets of β Y with ideals of C(Y).- 1 December 2022
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 72 (6) , 1429-1446
Ideals of functions with compact support in the integer-valued case
For a zero-dimensional Hausdorff space X, denote, as usual, by C(X, ℤ) the ring of continuous integer-valued functions on X. If f ∈ C(X, ℤ), denote by Z(f) the set of all points of X that are mapped to 0 by f. The set is the integer-valued analogue of the ideal of functions with compact support in C(X). By first working in the category of locales and then interpreting the results in spaces, we characterize this ideal in several ways. Writing ζ X for the Banaschewski compactification of X, we also explore some properties of ideals of C(X, ℤ) associated with subspaces of ζ X analogously to how one associates, for any Tychonoff space Y, subsets of β Y with ideals of C(Y).- 31 August 2022
- Published by Institute of Mathematics, Czech Academy of Sciences in Mathematica Bohemica
- Vol. 148 (4) , 481-500
On locales whose countably compact sublocales have compact closure
Institute of Mathematics of the Czech Academy of Sciences
- 31 August 2022
- Published by Institute of Mathematics, Czech Academy of Sciences in Mathematica Bohemica
- Vol. 148 (4) , 481-500
On locales whose countably compact sublocales have compact closure
Institute of Mathematics of the Czech Academy of Sciences