• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.469-474
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• 2015

In this paper, we will consider the notions of (m, n)-potent conditions in near-rings, in particular, a near-ring R with left bipotent or right bipotent condition. We will derive some properties of near-rings with (1, n) and (n, 1)-potent conditions where n is a positive integer, and then some properties of near-rings with (m, n)-potent conditions. Also, we may discuss the behavior of R-subgroups in (1, n)-potent or (n, 1)-potent near-rings..

• East Asian mathematical journal
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• v.25 no.4
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• pp.441-447
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• 2009

Jat and Choudhari defined a near-ring R with left bipotent or right bipotent condition in 1979. Also, we can dene a near-ring R as subcommutative if aR = Ra for all a in R. From these above two concepts it is natural to investigate the near-ring R with the properties aR = $Ra^2$ (resp. $a^2R$ = Ra) for each a in R. We will say that such is a near-ring with (1,2)-potent condition (resp. a near-ring with (2,1)-potent condition). Thus, we can extend a general concept of a near-ring R with (m,n)-potent condition, that is, $a^mR\;=\;Ra^n$ for each a in R, where m, n are positive integers. We will derive properties of near-ring with (1,n) and (n,1)-potent conditions where n is a positive integer, any homomorphic image of (m,n)-potent near-ring is also (m,n)-potent, and we will obtain some characterization of regular near-rings with (m,n)-potent conditions.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.587-606
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• 2017

This paper is a continuation of study semi-potentness endomorphism rings of module. We give some other characterizations of endomorphism ring to be semi-potent. New results are obtained including necessary and sufficient conditions for the endomorphism ring of semi(injective) projective module to be semi-potent. Finally, we characterize a module M whose endomorphism ring it is semi-potent via direct(injective) projective modules. Several properties of the endomorphism ring of a semi(injective) projective module are obtained. Besides to that, many necessary and sufficient conditions are obtained for semi-projective, semi-injective modules to be semi-potent and co-semi-potent modules.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.519-526
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• 2005

In this paper, we prove that every exchange ring can be characterized by potent elements. Also we extend [10, Theorem 3.1 and Theorem 4.1] to quasi-clean rings in which every element is a sum of a potent element and a unit.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1841-1850
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• 2014

It is known that the ranks of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$ (the semigroups of orientation preserving singular self-maps, partial and strictly partial transformations on $X_n={1,2,{\ldots},n}$, respectively) are n, 2n and n + 1, respectively. The idempotent rank, defined as the smallest number of idempotent generating set, of $\mathcal{SOP}_n$ and $\mathcal{SSPOP}_n$ are the same value as the rank, respectively. Idempotent can be seen as a special case (with m = 1) of m-potent. In this paper, we investigate the m-potent ranks, defined as the smallest number of m-potent generating set, of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$. Firstly, we characterize the structure of the minimal generating sets of $\mathcal{SOP}_n$. As applications, we obtain that the number of distinct minimal generating sets is $(n-1)^nn!$. Secondly, we show that, for $1{\leq}m{\leq}n-1$, the m-potent ranks of the semigroups $\mathcal{SOP}_n$ and $\mathcal{SPOP}_n$ are also n and 2n, respectively. Finally, we find that the 2-potent rank of $\mathcal{SSPOP}_n$ is n + 1.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.161-167
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• 2008

A ring R is called an $I_0$-ring if each left ideal not contained in the Jacobson radical J(R) contains a non-zero idempotent. If, in addition, idempotents can be lifted modulo J(R), R is called an I-ring or a potent ring. We study whether these properties are inherited by some related rings. Also, we investigate the structure of potent rings.

• Korean Journal of Pharmacognosy
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• v.30 no.2
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• pp.111-114
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• 1999

Inhibitory effect of water and ethyl acetate extract of 60 kinds of herbal medicines was investigated on ${\beta}-glucuronidase$. Among water extract of them, Galla Rhois had the most potent ${\beta}-glucuronidase-inhibitory\;activity$. Termaliae Fructus, Amomi Tsa-ko Fructus and Arecae Semen were also potent inhibitors. Among ethyl acetate extract of them, Galla Rhois had the most potent ${\beta}-glucuronidase-inhibitory\;activity$. Nelumbinis Semen. Ephedrae Radix and Termaliae Fructus were also potent inhibitors. The extract of Galla Rhois had potent hepatoprotective effect on $CCl_4-induced$ hepatotoxicity of rats. These results suggest that the ${\beta}-glucuronidase$ seems to be closely related to the liver injury, which could be prevented by the inhibitor of ${\beta}-glucuronidase$.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.401-409
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• 2000

In this paper, we determine the structure of ${\kappa}-potent$ elements and regular elements of the semigroup ${\Omega}_n$of doubly stochastic matrices of order n. In connection with this, we find the structure of the matrices X satisfying the equation AXA = A. From these, we determine a condition of a doubly stochastic matrix A whose Moore-Penrose generalized is also a doubly stochastic matrix.

• Proceedings of the PSK Conference
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• 2003.10b
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• pp.184.2-184.2
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• 2003

Many naturally occurring polyhydroxylated sterols and oxysterols exhibit potent biologic activities. The role of oxycholesterol including 2, 5(R)-2, 6-hydroxycholesterol is a potent inhibitor of cholesterol biosynthesis in vitro as it is an effective inhibitor of HMG-Coa reductase. Some new polyhydroxylated sterols were showed potent cytotoxicity to cancer cells. And it has also been chown to be an inhibitor of DNA synthesis, In order to synthesize the various oxy derivatives, we tried to positionselective and reagentselective epoxidation and reduction of cholesterol derivatives. (omitted)

• Proceedings of the Korean Society of Applied Pharmacology
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• 1997.04a
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• pp.12-12
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• 1997

CFC-222 is a novel fluoroqinolone antibacterial agent synthesized and under development by the Cheil Jedang Corporation, Korea. CFC-222 exerts the antibacterial activity by inhibition of bacterial DNA gyrase leading to bactericidal action. In in vitro and in vivo preclinical testing, CFC-222 has been shown to possess a broad spectrum of antibacterial activity. In particular CFC-222 is very potent against Gram-positive bacteria such as Staphylococcus spp., Streptocuccus spp. (in particular penicillin G-resistant and -susceptible S. pneumoniae) and Enterococcus spp. when compared to other quinolones (ciprofloxacin, ofloxacin or lomefloxacin). CFC-222 also showed potent activity against the methicillin resistant clinical isolates of S. aureus (MRSA). Against Gram-negative bacteria (E. coli, Pseudomonas and Sarcina) the activity of CFC-222 was slightly weaker than that of ciprofloxacin, but was more potent than that of ofloxacin or lomefloxacin. In urinary systemic infections caused by both Gram-positive and -negative bacteria, CFC-222 demonstrated a potent therapeutic efficacy in particular against Cram-positive bacteria S. aureus, S. pyrogen 203 and S. pneumonia TypeIII.