• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.531-542
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• 2014

In this paper, we apply some properties of reversible rings, Baerness of fixed rings, skew group rings and Morita Context rings to get conditions that shows fixed rings, skew group rings and Morita Context rings are reversible. Moreover, we investigate conditions in which Baer rings are reversible and reversible rings are Baer.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1069-1078
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• 2019

Let R be a ring with identity and P(R) denote the prime radical of R. An element r of a ring R is called strongly P-clean, if there exists an idempotent e such that $r-e=p{\in}P$(R) with ep = pe. In this paper, we determine necessary and sufficient conditions for an element of a trivial Morita context to be strongly P-clean.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.91-99
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• 2003

In this paper, we show that if the ring of a Merits context (A, B, M, N, ${\psi},\;{\phi}$) with zero pairings is a strongly $\pi$-regular ring of bounded index if and only if so are A and B. Furthermore, we extend this result to the ring of a Merits context over quasi-duo strongly $\pi$-regular rings.

• The Pure and Applied Mathematics
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• v.30 no.1
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• pp.15-24
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• 2023

In this paper, we show that bounded Hochschild homology and cohomology of associated matrix Banach algebra 𝔊(𝔄, R, S, 𝔅) to a Morita context 𝔐(𝔄, R, S, 𝔅, { }, [ ]) are isomorphic to those of the Banach algebra 𝔄. Consequently, we indicate that the n-amenability and simplicial triviality of 𝔊(𝔄, R, S, 𝔅) are equivalent to the n-amenability and simplicial triviality of 𝔄.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.247-261
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• 2010

An associative ring R with identity is called a clean ring if every element of R is the sum of a unit and an idempotent. In this paper, we introduce the concept of f-clean rings. We study various properties of f-clean rings. Let C = $\(\array{A\;V\\W\;B}\)$ be a Morita Context ring. We determine conditions under which the ring C is f-clean. Moreover, we introduce the concept of rings having many full elements. We investigate characterizations of this kind of rings and show that rings having many full elements are closed under matrix rings and Morita Context rings.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.267-276
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• 2017

In this paper we introduce rings that satisfy regular 1-stable range. These rings are left-right symmetric and are generalizations of unit 1-stable range. We investigate characterizations of these kind of rings and show that these rings are closed under matrix rings and Morita Context rings.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.277-285
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• 2017

In the various module generalizations of the concepts of prime (semiprime) for a ring, the question "when are semiprime modules subdirect product of primes?" is a serious question in this context and it is considered by earlier authors in the literature. We continue study on the above question by showing that: If R is Morita equivalent to a right pre-duo ring (e.g., if R is commutative) then weakly compressible R-modules are precisely subdirect products of prime R-modules if and only if dim(R) = 0 and R/N(R) is a semi-Artinian ring if and only if every classical semiprime module is semiprime. In this case, the class of weakly compressible R-modules is an enveloping for Mod-R. Some related conditions are also investigated.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.733-744
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• 2020

Let 𝕽 be a commutative ring with unity, A and B be 𝕽-algebras, M be a (A, B)-bimodule and N be a (B, A)-bimodule. The 𝕽-algebra 𝕾 = 𝕾(A, M, N, B) is a generalized matrix algebra defined by the Morita context (A, B, M, N, 𝝃_MN, Ω_NM). In this article, we study generalized derivation and generalized Jordan derivation on generalized matrix algebras and prove that every generalized Jordan derivation can be written as the sum of a generalized derivation and antiderivation with some limitations. Also, we show that every generalized Jordan derivation is a generalized derivation on trivial generalized matrix algebra over a field.