The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “The nil radical of an Archimedean partially ordered ring with positive squares”

When is every order ideal a ring ideal?

Melvin Henriksen, Suzanne Larson, Frank A. Smith (1991)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A lattice-ordered ring ℝ is called an if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those f -rings ℝ such that ℝ / 𝕀 is contained in an f -ring with an identity element that is a strong order unit for some nil l -ideal 𝕀 of ℝ . In particular, if P ( ℝ ) denotes the set of nilpotent elements of the f -ring ℝ , then ℝ is an OIRI-ring if and only if ℝ / P ( ℝ ) is contained in an f -ring with an identity element that is a strong order unit. ...

Nil-clean and unit-regular elements in certain subrings of 𝕄 2 ( ℤ )

Yansheng Wu, Gaohua Tang, Guixin Deng, Yiqiang Zhou (2019)

Czechoslovak Mathematical Journal

Similarity:

An element in a ring is clean (or, unit-regular) if it is the sum (or, the product) of an idempotent and a unit, and is nil-clean if it is the sum of an idempotent and a nilpotent. Firstly, we show that Jacobson’s lemma does not hold for nil-clean elements in a ring, answering a question posed by Koşan, Wang and Zhou (2016). Secondly, we present new counter-examples to Diesl’s question whether a nil-clean element is clean in a ring. Lastly, we give new examples of unit-regular elements...

A note on semilocal group rings

Angelina Y. M. Chin (2002)

Czechoslovak Mathematical Journal

Similarity:

Let R be an associative ring with identity and let J ( R ) denote the Jacobson radical of R . R is said to be semilocal if R / J ( R ) is Artinian. In this paper we give necessary and sufficient conditions for the group ring R G , where G is an abelian group, to be semilocal.