ELEMENTARY
1. Equivalent definitions and generalizations for algebraic lattices
(2012).
2. Some self-dual notions for groups
(2012-13).
3. Subrings of matrix rings
(2014-15).
4. Units and nilpotent elements in corners
(2015).
5. A false problem
(2016).
6. 2 x 2 unipotent matrices
(2017).
7. Traces of powers of 2 x 2 matrices
(2017).
8. Different row rank and column rank for a matrix
(2017).
9. A characterization of Dedekind finite rings
(2017).
10. Idempotent reversible rings
(2017).
11. Abelian groups whose subgroups are endomorphic kernels
(2018).
12. Very strongly clean rings
(2018).
13. A fine element which is not exchange
(2019).
14. Units generated by idempotents
(2019).
15. Equivalent idempotents are conjugate in any ring
(2019).
16. Exercise in Fuchs 1973 and 2015
(2019).
17. "Everything" lifts modulo nil ideals
(2020).
18. GreatestCommonDivisor domains (corrected)
(2020).
19. Equivalent nilpotents may not be conjugate
(2020).
20. Matrices similar to transposes
(2020).
21. Zero determinants revisited
(2020).
22. Von Neumann regular matrices of small sizes over integral domains
(2020).
23. Idempotent sums of idempotents
(2020).
24. Idempotent von Neumann regular rings
(2020).
25. Left or right simple rings
(2020).
26. Idempotent matrices similar to triangular
matrices are also similar to diagonal matrices
(2020).
27. Equivalent tripotents may not be conjugate
(2020).
28. Strongly clean decompositions may not be unique
(2021).
29. Rings of characteristics 2 may not be Boolean
(2021).
30. Units in subrings with different identity "produce" units in the whole ring
(2021).
31. Square-zero matrices with nonzero determinant
(2021).
32. Unit-regular element have stable range one: A direct proof
(2021).
33. Strongly regular elements are unit-regular, an undergraduate proof
(2022).
34. From reduced rings to Dedekind finite rings
(2022).
35. Another definition of clean rings
(2022).
36. The rings all whose nil-clean elements are uniquely nil-clean are precisely the Abelian rings
(2022).
37. Square roots of quasiregular elements in a ring, are quasiregular
(2022).
38. Unit-regular elements and Jacobson radical
(2022).
39. Integral idempotent 2 x 2 matrices
(2023).
40. An exercise on isomorphic idempotents
(2023).
41. A rank zero nonzero matrix
(2023).
42. A property of gcd's
(2023).
43. The rings with commuting nilpotents are
Dedekind-finite; a direct proof
(2024).
44. The rings whose isomorphic idempotents are equal
(2024).
45. Any strongly regular ring is regular: an elementary proof
(2024).
46. Strongly regular rings have stable range one: a simple unitizer
(2024).
47. Fusible Abelian groups
(2024).
48. LZ-reduced Abelian groups
(2024).
49. A useful trick in (exchange) rings
(2024).