Abstract.A module M is called poor whenever it is N-injective, then the module N is semisimple. In this paper the properties of poor modules are investigated and are used to characterize various families of rings. Warmly dedicated to Patrick F. Smith on the occasion of his 65th birthday.2000 Mathematics Subject Classification. 16D50, 16D70.

Fast and simple CAD‐oriented analytical expressions for the characteristic impedance and the effective permittivity of asymmetric coplanar waveguides and coplanar strip lines are derived using the conformal mapping method. It has been found that the results calculated using analytical expressions obtained in the present article are in very good agreement with the analytical and experimental results given in the literature. The formulas derived in this study have also been verified to be valid for symmetric coplanar waveguide and strip lines. © 1995 John Wiley & Sons, Inc.

In this study the effects of compound B1, bis(3-aryl-3-oxo-propyl)methylamine hydrochloride, and an antiinflammatory drug, indomethacin, were tested by carrageenan-induced paw edema and cotton pellet granuloma tests, for effects on acute and chronic phases of inflammation, respectively. Their effects on vascular permeability were also determined by hyaluronidase-induced capillary permeability test. Anti-inflammatory activity of B1 was compared with indomethacin. B1 decreased the carrageenan-induced paw edema by 49%, 35%, and 47% at 50, 100, and 200 mg kg ؊1 doses, respectively, while this decrease was 82% by indomethacin at 20 mg kg ؊1 dose. Antiproliferative effects in cotton pellet test of B1 at 50 mg kg ؊1 and indomethacin at 20 mg kg ؊1 doses were 44% and 43%, respectively. Indomethacin but not B1 inhibited the hyaluronidase-induced increase in capillary permeability. Our results suggest that B1 inhibits both acute and chronic phases of inflammation probably by an effect not mediated by prevention of increased capillary permeability. Especially, its anti-inflammatory activity against chronic phase of inflammation was comparable with that of indomethacin. Further detailed studies are needed to clarify the mechanism(s) of action responsible for the anti-inflammatory activity of B1.

Communicated by Louis Rowen MSC: 16D50 16D60 16D80 16N20 16N60 Keywords: Second submodule Second radical Prime submodule Prime radical Socle of a moduleIn this article, we study the second radical of a module over an arbitrary ring R as the dual notion of the prime radical of a module. We give some properties of the second radical and determine the second radical of some modules. We define the notion of m * -system and describe the second radical of submodules in terms of m * -systems. We investigate when the second radical of a module M is equal to the socle of M. In particular, we give a characterization of the socle of a noetherian module over a ring R such that the ring R/P is right artinian for every right primitive ideal P by using the concept of second radical. We also give a characterization of right quasi-duo artinian rings by using the second radical of an injective module.

Let M be a left R-module and F a submodule of M for any ring R. We call M F-semiregular if for every x 2 M, there exists a decomposition M ¼ A È B such that A is projective, A Rx and Rx \ B F. This definition extends several notions in the literature. We investigate some equivalent conditions to F-semiregular modules and consider some certain fully invariant submodules such as ZðMÞ; SocðMÞ; dðMÞ. We prove, among others, that if M is a finitely generated projective module, then M is quasi-injective if and only if M is ZðMÞ-semiregular and M È M is CS. If M is projective SocðMÞ-semiregular module, then M is semiregular. We also characterize QF-rings R with JðRÞ 2 ¼ 0.

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In this article, we consider the module theoretic version of I-semiperfect rings R for an ideal I which are defined by Yousif and Zhou (2002). Let M be a left module over a ring R, N ∈ M , and M a preradical on M . We call N M -semiperfect in M if for any submodule K of N , there exists a decomposition K = A ⊕ B such that A is a projective summand of N in M and B ≤ M N . We investigate conditions equivalent to being a M -semiperfect module, focusing on certain preradicals such as Z M Soc, and M . Results are applied to characterize Noetherian QF-modules (with Rad M ≤ Soc M ) and semisimple modules. Among others, we prove that if every R-module M is Soc-semiperfect, then R is a Harada and a co-Harada ring.

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