What question did this study set out to answer?

The aim is to define and explore left weakly Baer rings and their properties, especially their relation to polynomial extensions.

June 14, 2026Open Access

Weakly Baer Rings

Key Points

The aim is to define and explore left weakly Baer rings and their properties, especially their relation to polynomial extensions.
Defined the left weakly Baer property for rings with unity.
Analyzed the implications of this property on the flatness of modules.
Provided examples to illustrate the findings.
Demonstrated that left weakly Baer rings have specific properties distinct from Baer and right PP conditions.
Confirmed that polynomial extensions inherit the weakly Baer property.

Abstract

We say a ring R with unity is left weakly Baer if the left annihilatorof any nonempty subset of R is right s-unital by right semicentral idempotents,which implies that R modulo the left annihilator of any nonempty subset isﬂat. It is shown that, unlike the Baer or right PP conditions, the weaklyBaer property is inherited by polynomial extensions. Examples are providedto explain the results.

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