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The objective is to introduce and study JU rings, along with their notable properties and connections to other ring classes.

April 1, 2026Open Access

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Rings with Jacobson units

PDPeter V. Danchev

Key Points

The objective is to introduce and study JU rings, along with their notable properties and connections to other ring classes.
Introduction of the concept of JU rings.
Comparison with UU rings and their properties.
Proving that any exchange JU ring is semi-boolean and vice versa.
Establishment of the property that exchange JU rings are semi-boolean.
Extension of previous results related to JU and UU rings.
Identification of significant characteristics unique to JU rings.

Abstract

We introduce and study the notion of JU rings, that are, rings having only Jacobson units. In parallel to the so-called UU rings, these rings also form a large class and have many interesting properties established in the present paper. For instance, it is proved that any exchange JU ring is semi-boolean, and vice versa. This somewhat extends a result due to Lee-Zhou (Glasg. Math. J., 2008) and Danchev-Lam (Publ. Math. Debrecen, 2016).

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Peter V. Danchev (Fri,) studied this question.

synapsesocial.com/papers/69cd7a815652765b073a7c2b https://doi.org/https://doi.org/10.15099/00016932

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