• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.419-430
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• 2005

In this paper, we introduce the notions of ($\in,\;{\in} V q$)-fuzzy subnear-ring, ($\in,\;{\in} V q$)-fuzzy ideal and ($\in,\;{\in}V q$)-fuzzy quasi-ideal of near-rings and find more generalized concepts than those introduced by others. The characterization of such ($\in,\;{\in}V q$)-fuzzy ideals are also obtained.

• Kyungpook Mathematical Journal
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• 제18권1호
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• pp.23-29
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• 1978

In [7) Scott has defined C-formation radical for a class C of near rings and has studied its porperties under chain conditions. A natural question that arises is: Does there exist a Lower C-Formation radical class L(M) containing a given class M of ideals of near rings in C? In this paper we answer this by giving. two constructions for L(M) and prove that prime radical is hereditary.

• Kyungpook Mathematical Journal
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• 제50권3호
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• pp.379-387
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• 2010

In this paper, we present some results concerning orthogonal generalized (${\sigma},{\tau}$)-derivations in semiprime near-rings. These results are a generalization of result of Bresar and Vukman, which are related to a theorem of Posner for the product of two derivations in prime rings.

• East Asian mathematical journal
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• 제30권3호
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• pp.259-270
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• 2014

For a generalized triangular matrix ring $$T=\[\array{R\;M\\0\;S}]$$, over rings R and S having only the idempotents 0 and 1 and over an (R, S)-bimodule M, we characterize all homomorphisms ${\alpha}$'s and all ${\alpha}$-derivations of T. Some of the homomorphisms are compositions of an inner homomorphism and an extended or a twisted homomorphism.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.343-347
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• 2016

Posner's first theorem states that if R is a prime ring of characteristic different from two, $d_1$ and $d_2$ are derivations on R such that the iterate $d_1d_2$ is also a derivation of R, then at least one of $d_1$, $d_2$ is zero. In the present paper we extend this result to *-prime rings of characteristic different from two.

• 대한수학회지
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• 제44권4호
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• pp.987-995
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• 2007

We investigate some results which concern the types of Noetherian local rings. In particular, we show that if r(Ap) ${\le}$ depth Ap + 1 for each prime ideal p of a quasi-unmixed Noetherian local ring A, then A is Cohen-Macaulay. It is also shown that the Kawasaki conjecture holds when dim A ${\le}$ depth A + 1. At the end, we deal with some analogous results for modules, which are derived from the results studied on rings.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.767-777
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• 2019

We present a new way of obtaining the complete factorization of $X^n-1$ for n = 15, 17, 19 over the 4-adic ring ${\mathcal{O}}_4[X]$ of integers and thus over the Galois rings $GR(2^e,2)$. As a result, we determine all cyclic codes of lengths 15, 17 and 19 over those rings. This extends our previous work on such cyclic codes of odd lengths less than 15.

• 호남수학학술지
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• 제41권2호
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• pp.321-328
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• 2019

We completely characterize the isomorphic class of those associative unitary rings whose elements are sums of four commuting idempotents. Our main theorem enlarges results due to Hirano-Tominaga (Bull. Austral. Math. Soc., 1988), Tang et al. (Lin. & Multilin. Algebra, 2019), Ying et al. (Can. Math. Bull., 2016) as well as results due to the author in (Alban. J. Math., 2018), (Gulf J. Math., 2018), (Bull. Iran. Math. Soc., 2018) and (Boll. Un. Mat. Ital., 2019).

• 대한수학회보
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• 제59권1호
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• pp.213-226
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• 2022

Let R be a ring and M an R-module. Then M is said to be regular w-flat provided that the natural homomorphism I ⊗_R M → R ⊗_R M is a w-monomorphism for any regular ideal I. We distinguish regular w-flat modules from regular flat modules and w-flat modules by idealization constructions. Then we give some characterizations of total quotient rings and Prüfer v-multiplication rings (PvMRs for short) utilizing the homological properties of regular w-flat modules.

• 대한수학회논문집
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• 제37권3호
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• pp.659-667
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• 2022

This paper treats the commutativity of prime rings with involution over which elements satisfy some specific identities involving endomorphisms. The obtained results cover some well-known results. We show, by given examples, that the imposed hypotheses are necessary.