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Some Results on W-regular Rings
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Von Neumann regular rings, introduced in 1936, form a cornerstone of abstract algebra and were later extended to weakly regular rings. This work considers another extension, the W-regular rings defined by Wei [6], and explores their properties and distinctions from related notions.The present paper looks into the characterizations of a few fundamental qualities of W-regular rings. We prove that if is a W-regular ring and for all, then H is a W-regular. If is an NI-ring and be a regular ring, then be a W-regular ring if is n-regular. A ring is a W-regular ring if and only if is a direct summand for all. If is a ring with every right simple singular H-module is np-injective, is semiprime ring and an N-duo, then is a W-regular.
Title: Some Results on W-regular Rings
Description:
Von Neumann regular rings, introduced in 1936, form a cornerstone of abstract algebra and were later extended to weakly regular rings.
This work considers another extension, the W-regular rings defined by Wei [6], and explores their properties and distinctions from related notions.
The present paper looks into the characterizations of a few fundamental qualities of W-regular rings.
We prove that if is a W-regular ring and for all, then H is a W-regular.
If is an NI-ring and be a regular ring, then be a W-regular ring if is n-regular.
A ring is a W-regular ring if and only if is a direct summand for all.
If is a ring with every right simple singular H-module is np-injective, is semiprime ring and an N-duo, then is a W-regular.
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