Nakayama Rings Research Articles

A note on essential Ikeda–Nakayama rings

A note on essential Ikeda–Nakayama rings

A Note on Co-Harada Rings

In the early 1990s, Harada and Oshiro introduced extending and lifting properties for modules and, simultaneously, considered two new classes of artinian rings which contain quasi-Frobenius (QF-) rings and Nakayama rings: one is the class of right Harada rings and the other is the class of right co-Harada rings. Although QF-rings and Nakayama rings are left-right symmetric, Harada and co-Harada rings are not left-right symmetric. However, Oshiro showed that left Harada rings and right co-Harada rings are coinside. In this paper we provide many characterizations of right co-Harada rings and (right and left) co-Harada rings.

Kidney transplantation in diabetic recipients with iliac atherosclerosis: Arterial anastomosis with Nakayama's ring pin stapler after endarterectomy

To report our experience of arterial anastomosis with Nakayama's ring pin staplers (titanium staplers) after an endarterectomy in kidney transplantation of diabetic recipients with iliac atherosclerosis. In a series of 2126 kidney transplantations carried out between January 1998 and December 2008, 62 recipients received an endarterectomy during transplantation before renal arterial anastomoses as a result of severe iliac atherosclerosis. The renal arteries were anatomosed to hypogastric arteries through titanium staplers in 32 patients (group 1), or to external/common iliac arteries with conventional suturing in 30 patients (group 2). Perioperative outcomes of the two groups have been compared. The mean artery anastomosis time in group 1 was considerably shorter than in the group 2 (6.4 min vs 17.3 min, P < 0.001). Group 1 showed a lower rate of delayed graft function (4.8% vs 27.5%, P = 0.004). No difference in Kaplan-Meier patient survival rate was found between group 1 and group 2 after follow up of 67 ± 28 months (P = 0.58). Graft survival rate (patient deaths included) was higher in group 1 than in group 2 (P = 0.04). Arterial anastomosis with a titanium stapler is more rapid than conventional suture. It can diminish the rate of delayed graft function and improve the graft survival rate in diabetic recipients with severe iliac atherosclerosis.

On Nakayama Rings#

Fuller [Fuller, K. R. (1969). On indecomposable injectives over artinian rings. Pacific J. Math. 29:115–135] has proved that a right artinian ring is a right Nakayama and right co-Nakayama ring if and only if it is a two-sided Nakayama artinian ring. Oshiro [Oshiro, K. (1989). On Harada rings I. Math. J. Okayama Univ. 31:161–178] has proved that a right artinian ring is a right Nakayama QF-3 ring if and only if it is a two-sided Nakayama artinian ring. These results poses a question whether a right co-Nakayama ring and right QF-3 ring is two-sided Nakayama artinian. First Theorem 1.4 proves this question affirmatively. Next using this result and properties of one-sided Harada rings, we shall give some characterizations of Nakayama rings.

Ikeda–Nakayama Rings

A ring R is called a right Ikeda-Nakayama ring (right IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the two left annihilators. In this paper we show that if R is a right IN-ring and A and B are right ideals of R that are complements of each other, there exists an idempotent e in R such that A=eR and B=(1−e)R. As a consequence we show that R is right selfinjective if and only if M2(R) is a right IN-ring. It is also shown that R is a dual ring if and only if R is a left and right IN-ring and the dual of every simple right R-module is simple. Finally, we prove that R is quasi-Frobenius if and only if R is a left perfect, left and right IN-ring, extending work on both selfinjective rings and dual rings. Several examples are provided to show that our results are non-trivial extensions of the known results on the subject.

A characterization of nakayama rings

(1995). A characterization of nakayama rings. Communications in Algebra: Vol. 23, No. 2, pp. 739-741.

Characterizations of right Nakayama rings

We have studied relationships between almost relative projectivity and Nakayamaings [8]. In this paper we shall further investigate certain characterizations of right Nakayama rings in terms of almost relative projectives (or injectives). We shall consider three conditions (A), (B) and (C) (see Section 1), which are always satisfied for the relative projective modules, but not for almost relative projectives in general. As an application of [9, Theorem] and [10, Theorem 2], we shall show that a right artinian ring is right Nakayama if and only if one of the above three conditions holds true for almost relative projectives (Corollary to Theorem 1). Moreover we shall give a characterization of two-sided Nakayama rings related to (C) and the dual (C#) (Theorem 2). Finally we shall investigate the transitivity of almost relative projectives, which is the converse of (B), and give some characterizations of right Nakayama rings related to the transitivity.

Almost M-projectives and nakayama rings

In 1960, H. Bass [3] defined the notion of semi-perfect rings and, in 1963, E. Mares [l l] generalized it to that of semi-perfect modules. Since that time various kinds of further generalizations have been considered. In particular, K. Oshiro [ 161 studied quasi-semiperfect modules in connection with several important conditions on direct summands. The present paper is closely related to his paper as well as to the papers [ 12, 151 by Mueller and others and is cncerned with the condition (D,) (which is (C,) in [16]) over modules with direct decomposition into hollow modules. This is indeed motivated by the theorem [ 16, Theorem 3.51 that every quasisemiperfect module has the above type of decomposition. In Section 2 we shall clarify relationships between M-projectives over modules with direct decomposition into hollow modules and the condition (D,), which is dual to Cl.5, Theorem 81. In order to translate (D, ) in terms of homomorphisms, we shall introduce a new concept of almost A4-projectives to find some relations between almost M-projectives and a weaker condition (D’,). After preparing several basic results in Section 3, we shall, in Section 4, restrict ourselves to semi-perfect rings and give a series of characterizations of right Nakayama rings with special properties by making use of the concept of almost M-projectives. Finally, we shall classify modules with (D,) over a local Dedekind domain in Section 5.

Generalizations of Nakayama ring. VII. Hereditary rings

Generalizations of Nakayama ring. VII. Hereditary rings

Generalizations of Nakayama ring. IV. Left serial rings with (*,1)

Generalizations of Nakayama ring. IV. Left serial rings with (*,1)

Generalizations of Nakayama ring. II

Generalizations of Nakayama ring. II

Blood flow and scanning electron microscope study on venous microvascular anastomoses with Nakayamas apparatus and manual suture.

Endothelium repair and blood flow changes after microvascular anastomoses in rabbit neck veins (diameter 1.5-2.5 mm) with either Nakayamas apparatus or manual suture were studied with scanning electron microscope and electromagnetical flowmeter. The healing process, which was very rapid, was examined at varying intervals from the day of surgery to four weeks postoperatively. Complete endothelialization was evident after one week. The blood flow was unimpaired by anastomosis with Nakayama rings, whereas in the suture group reduction in blood flow followed immediately after surgery. This reduction was however transient and blood flow was normalized two hours postoperatively.

Microvascular Surgery

In situations where existing techniques of reconstruction are inadequate or involve multiple stages, free-flap transfer offers major advantages for the head and neck surgeon. Wider application of free-flap surgery has been inhibited by problems of flap design and graft take. Thrombosis at the microanastomic site, particularly at the venous site, is still a cause of failure. Techniques of anastomosis are of paramount importance. Nakayama ring pin anastomosis is easier to learn, less time-consuming, and shows less early thrombosis that suture techniques. Use of adjunctive pharmacologic agents, such as the tetrahydroimidazo quinazolines, will increase the likelihood of success.

The effect of dextran on the incidence of thrombosis in microvenous Nakayama ring pin anastomoses. Including further studies on the histopathology of Nakayama anastomoses.

Anastomoses of the posterior facial veins in the rabbits neck (diameter appr. 1.5-2.0 mm) were performed under the operating microscope, using the Nakayama ring pin stapler. Immediately before the operation the animals received clinical dextran (mw 70000) or physiological saline intravenously in a double-blind randomized pattern. The total incidence of partial or complete thrombosis in this experiment was low (around 10%). No difference between the two groups were detected. All anastomoses were examined in vivo, under the microscope and histologically. The histological findings are penetrated.

Anastomosis of Small Veins with Suture or Nakayama's Apparatus

In controlled experiments, the posterior facial veins in the rabbits neck (diameter 1.5-2.0 mm) were repaired, either by manual suture with 10-0 nylon or by the use of Nakayama's ring pin stapler. The so-called Nakayama "animal" rings, made from metal alloy, as well as the "human" rings, made from tantalum, were employed. A Nakayama anastomosis was performed in only one-third of the time required to complete a suture anastomosis. Evaluation of anastomotic patency was carried out after 7 days, and the vessels were examined histologically in serial sections. Veins anastomosed by the Nakayama technique had a statistically significant lower rate of early thrombosis than the sutured veins, while no difference was found in the occurrence of late thrombosis. The histological analysis showed a perfect endothelium-to-endothelium coaptation in the Nakayama anastomoses, and endothelium covered the anastomotic site in one week. In suture anastomoses the histological picture was more complex, with disintegration of the layers of the vessel wall and hyaline degeneration betweeen sutures. The "animal" rings almost constantly caused local phlebitis, but these changes were not reflected in the patency rates at one week.