• Kyungpook Mathematical Journal
• /
• 제54권3호
• /
• pp.471-476
• /
• 2014

Let R be a ring. A right R-module M is PS-injective if every R-homomorphism $f:aR{\rightarrow}M$ for every principally small right ideal aR can be extended to $R{\rightarrow}M$. We investigate, in this paper, rings whose simple singular modules are PS-injective. New characterizations of semiprimitive rings and semisimple Artinian rings are given.

• Journal of the Korean Data and Information Science Society
• /
• 제18권3호
• /
• pp.827-832
• /
• 2007

Several partial orders on integral partitions have been studied with many applications such as majorizations, capacities of quantum memory and embeddabilities of matrix algebras. In particular, the embeddability, stable embeddability and strong-stable embeddability problems arise for finite dimensional irreducible modules over a complex simple Lie algebra L. We find a sufficient condition for an L-module strong-stably embeds into another L-module using formal character theory.

• 대한수학회지
• /
• 제32권2호
• /
• pp.265-277
• /
• 1995

In [9], we gave a very explicit description of the injective envelope of an arbitray simple module over a polynomial ring $K[X_1, \ldots, X_n]$ over a field K in indeterminates $X_1, \ldots, X_n$. This paper presents another approach to give a description.

• 대한수학회보
• /
• 제37권1호
• /
• pp.1-19
• /
• 2000

We investigate in this paper the maximality of prime ideals in rings whose simple singular left R-modules are p-injective.

• 대한수학회지
• /
• 제50권5호
• /
• pp.1051-1066
• /
• 2013

By utilizing known characterizations of ${\omega}$-Noetherian rings in terms of injective modules, we give more characterizations of ${\omega}$-Noetherian rings. More precisely, we show that a commutative ring R is ${\omega}$-Noetherian if and only if the direct limit of GV -torsion-free injective R-modules is injective; if and only if every R-module has a GV -torsion-free injective (pre)cover; if and only if the direct sum of injective envelopes of ${\omega}$-simple R-modules is injective; if and only if the essential extension of the direct sum of GV -torsion-free injective R-modules is the direct sum of GV -torsion-free injective R-modules; if and only if every $\mathfrak{F}_{w,f}(R)$-injective ${\omega}$-module is injective; if and only if every GV-torsion-free R-module admits an $i$-decomposition.

• Journal of the Optical Society of Korea
• /
• 제8권2호
• /
• pp.55-58
• /
• 2004

Several internal wavelength locker schemes for 10 Gbps electro-absorption modulated laser EML) module were reviewed. 10 Gbps EML modules with simple and robust internal wavelength ockers for metro dense WDM application were successfully demonstrated. The wavelength aging ver 2000 hours was done at elevated temperature of 7$0^{\circ}C$. The average wavelength drift of 10 modules was measured to be about $\pm$ 5 pm. These modules can be successfully applied to the 0 Gbps DWDM systems with 50 ㎓ channel spacing.

• 대한수학회보
• /
• 제56권6호
• /
• pp.1617-1642
• /
• 2019

In this paper, we study a theory for the structure of ${\tau}_w$-Loewy series of modules over commutative rings, where ${\tau}_w$ is the hereditary torsion theory induced by the so-called w-operation, and explore the relationship between ${\tau}_w$-Loewy modules and w-Artinian modules.

• 호남수학학술지
• /
• 제43권3호
• /
• pp.403-416
• /
• 2021

It is known that the rank 2 stably free syzygy module P⁽²⁾ is not free. This algebraic fact was proved analytically, but this remarkable fact still lacks of a simple algebraic proof. The main purpose of this paper is to give a partially algebraic proof by making use of a theorem whose proof is quite topological, and the further properties of the module will be discussed.

• 호남수학학술지
• /
• 제29권2호
• /
• pp.269-277
• /
• 2007

Let L := L(G) denote the classical modular Lie algebra of $E_6$-type over an algebraically closed field F of characteristic p > 5 associated with some simple and simply connected algebraic group G. After the prototypes of those for $E_8$-type in [4], we shall search for irreducible (=simple) L-modules in this paper.

• 대한수학회보
• /
• 제32권2호
• /
• pp.191-200
• /
• 1995

Simple Lie albegras over algebraically closed field with characteristic p > 7 were classified by H. Strade and R. L. Wilson in 1991 [7]. All modular representations of simple Lie algebras, however, are not classified although some restricted modular representations have been done earlier by Curtis and Steinberg. In connection with this, we would like to decompose basic $sp_4$(F)-modules $sl_4$-(F) and $gl_4$(F) over nonzero characteristic by way of characteristic zero case.