Rings in which each finitely generated right ideal is automorphism-invariant (right[Formula: see text]-rings) are shown to be isomorphic to a formal matrix ring. Among other results it is also shown that (i) if [Formula: see text] is a right nonsingular ring and [Formula: see text] is an integer, then [Formula: see text] is a right self injective regular ring if and only if the matrix ring [Formula: see text] is a right [Formula: see text]-ring, if and only if [Formula: see text] is a right automorphism-invariant ring and (ii) a right nonsingular ring [Formula: see text] is a right [Formula: see text]-ring if and only if [Formula: see text] is a direct sum of a square-full von Neumann regular right self-injective ring and a strongly regular ring containing all invertible elements of its right maximal ring of fractions. In particular, we show that a right semiartinian (or left semiartinian) ring [Formula: see text] is a right nonsingular right [Formula: see text]-ring if and only if [Formula: see text] is a left nonsingular left [Formula: see text]-ring.

The overuse of copper (Cu) fungicides has resulted in an accumulation of Cu in the orange-growing soil in Cao Phong district, Hoa Binh province. In this study, we analyzed the fractionation and accumulation of Cu in soils treated with two types of fungicides: Norshield 86.2WG  and Epolists 85WP. Using vetiver grass has been known as a approach to immobilize heavy metals in soil, herein, its effect on the fate of Cu was also considered. The bioavailability of Cu was relatively high for both the tested soils treated with Norshield 86.2WG  (~9.82-11.03%) and Epolists 85WP (~8.46-10.79%). Noting that Cu in different fractions increased following the order F1 (water soluble) < F2 (exchange adsorption) < F3 (special adsorption) < F4 (bound with Fe/Al hydroxide) < F5 (bound to organic matter) < F6 (remaining form). The use of vetiver grass resulted in different accumulation levels of Cu  between natural soil (9.5 ± 0.53 ppm) and Cu-added soils (from 16.17 ± 1.72 to 27.13 ± 1.31 ppm). The application of Norshield 86.2WG  and Epolists 85WP has exacerbated the contamination of soil by Cu, therefore, to manage and enhance soil health in this area, we need to consider reducing the use of fungicides in the orange-growing areas. Keywords: Cao Phong orange, fungicides, Cu pollution, Cu accumulation, Vetiver grass.

In this paper, we give some results of indecomposable rings in which finitely generated right ideals are automorphism-invariant. They are called [Formula: see text]-rings. It shows that any indecomposable right artinian right Rickart right [Formula: see text]-ring [Formula: see text] is Morita equivalent to a formal upper triangular matrix ring. Moreover, we also study endomorphism rings of automorphism-invariant modules.