• Tribology and Lubricants
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• v.12 no.4
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• pp.7-12
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• 1996

Present study was undertaken to investigate the leakage and friction of self-lubricating piston seal rings. A crank-piston type gas leakage test set-up was constructed. The piston rings were made of PTFE-polyimide composite. The free gap configurations of the seal rings were butt and step types. Eccentric tension rings were used to give the seal rings prepressure between the seal rings and cylinder wall. Two sizes of the tension rings were installed to investigate their effect on the gas leakage and friction of the seal rings. The results showed that step type seal rings are superior than the butt types. High tension spring rings resulted in low leakage and high friction loss. In order to reduce the gas leakage and friction loss of the piston seal rings, there should be compromise between the number of ring stages and prepressure of the tension rings.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.131-144
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• 2020

Characterizations of almost perfect domains by certain covers and envelopes, due to Bazzoni-Salce [7] and Bazzoni [4], are generalized to almost perfect commutative rings (with zero-divisors). These rings were introduced recently by Fuchs-Salce [14], showing that the new rings share numerous properties of the domain case. In this note, it is proved that admitting strongly flat covers characterizes the almost perfect rings within the class of commutative rings (Theorem 3.7). Also, the existence of projective dimension 1 covers characterizes the same class of rings within the class of commutative rings admitting the cotorsion pair (𝒫₁, 𝒟) (Theorem 4.1). Similar characterization is proved concerning the existence of divisible envelopes for h-local rings in the same class (Theorem 5.3). In addition, Bazzoni's characterization via direct sums of weak-injective modules [4] is extended to all commutative rings (Theorem 6.4). Several ideas of the proofs known for integral domains are adapted to rings with zero-divisors.

• The Pure and Applied Mathematics
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• v.10 no.3
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• pp.177-183
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• 2003

In this paper, we initiate the study of some annihilator conditions on polynomials which were used by Kaplansky [Rings of operators. W. A. Benjamin, Inc., New York, 1968] to abstract the algebra of bounded linear operators on a Hilbert spaces with Baer condition. On the other hand, p.p.-rings were introduced by Hattori [A foundation of torsion theory for modules over general rings. Nagoya Math. J. 17 (1960) 147-158] to study the torsion theory. The purpose of this paper is to introduce the near-rings with Baer condition and near-rings with p.p. condition which are somewhat different from ring case, and to extend a results of Armendariz [A note on extensions of Baer and P.P.-rings. J. Austral. Math. Soc. 18 (1974), 470-473] and Jøndrup [p.p. rings and finitely generated flat ideals. Proc. Amer. Math. Soc. 28 (1971) 431-435].

• 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.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.751-771
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• 2014

We study the structure of idempotents in polynomial rings, power series rings, concentrating in the case of rings without identity. In the procedure we introduce right Insertion-of-Idempotents-Property (simply, right IIP) and right Idempotent-Reversible (simply, right IR) as generalizations of Abelian rings. It is proved that these two ring properties pass to power series rings and polynomial rings. It is also shown that ${\pi}$-regular rings are strongly ${\pi}$-regular when they are right IIP or right IR. Next the noncommutative right IR rings, right IIP rings, and Abelian rings of minimal order are completely determined up to isomorphism. These results lead to methods to construct such kinds of noncommutative rings appropriate for the situations occurred naturally in studying standard ring theoretic properties.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1511-1528
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• 2020

A skew generalized power series ring R[[S, 𝜔]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action 𝜔 of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are skew polynomial rings, skew Laurent polynomial rings, skew power series rings, skew Laurent series rings, skew monoid rings, skew group rings, skew Mal'cev-Neumann series rings, the "untwisted" versions of all of these, and generalized power series rings. In this paper we obtain some necessary conditions on R, S and 𝜔 such that the skew generalized power series ring R[[S, 𝜔]] is (uniquely) clean. As particular cases of our general results we obtain new theorems on skew Mal'cev-Neumann series rings, skew Laurent series rings, and generalized power series rings.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.407-423
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• 2022

In this paper, we determine the structure of rings that have secondary representation (called representable rings) and give some characterizations of these rings. Also, we characterize Artinian rings in terms of representable rings. Then we introduce completely representable modules, modules every non-zero submodule of which have secondary representation, and give some necessary and sufficient conditions for a module to be completely representable. Finally, we define strongly representable modules and give some conditions under which representable module is strongly representable.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.93-108
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• 2011

A ring R is called left weakly np- injective if for each non-nilpotent element a of R, there exists a positive integer n such that any left R- homomorphism from $Ra^n$ to R is right multiplication by an element of R. In this paper various properties of these rings are first developed, many extending known results such as every left or right module over a left weakly np- injective ring is divisible; R is left seft-injective if and only if R is left weakly np-injective and $_RR$ is weakly injective; R is strongly regular if and only if R is abelian left pp and left weakly np- injective. We next introduce the concepts of left weakly pp rings and left weakly C2 rings. In terms of these rings, we give some characterizations of (von Neumann) regular rings such as R is regular if and only if R is n- regular, left weakly pp and left weakly C2. Finally, the relations among left C2 rings, left weakly C2 rings and left GC2 rings are given.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.1-21
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• 2015

C-domains are defined via class semigroups, and every C-domain is a Mori domain with nonzero conductor whose complete integral closure is a Krull domain with finite class group. In order to extend the concept of C-domains to rings with zero divisors, we study v-Marot rings as generalizations of ordinary Marot rings and investigate their theory of regular divisorial ideals. Based on this we establish a generalization of a result well-known for integral domains. Let R be a v-Marot Mori ring, $\hat{R}$ its complete integral closure, and suppose that the conductor f = (R : $\hat{R}$) is regular. If the residue class ring R/f and the class group C($\hat{R}$) are both finite, then R is a C-ring. Moreover, we study both v-Marot rings and C-rings under various ring extensions.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.289-309
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• 2019

This paper is intended as a discussion of some generalizations of the notion of a reversible ring, which may be obtained by the restriction of the zero commutative property from the whole ring to some of its subsets. By the INCZ property we will mean the commutativity of idempotent elements of a ring with its nilpotent elements at zero, and by ICZ property we will mean the commutativity of idempotent elements of a ring at zero. We will prove that the INCZ property is equivalent to the abelianity even for nonunital rings. Thus the INCZ property implies the ICZ property. Under the assumption on the existence of unit, also the ICZ property implies the INCZ property. As we will see, in the case of nonunital rings, there are a few classes of rings separating the class of INCZ rings from the class of ICZ rings. We will prove that the classes of rings, that will be discussed in this note, are closed under extending to the rings of polynomials and formal power series.