• 대한수학회논문집
• /
• 제18권2호
• /
• pp.225-233
• /
• 2003

In this paper, we obtain Hon(P,- ) is an exact functor if P is a p-projective BCI-algebra.

• 대한수학회논문집
• /
• 제35권2호
• /
• pp.469-480
• /
• 2020

Let R be a commutative ring with identity and M a unital R-module. We give a new generalization of exact sequences called e-exact sequences. A sequence $0{\rightarrow}A{\longrightarrow[20]^f}B{\longrightarrow[20]^g}C{\rightarrow}0$ is said to be e-exact if f is monic, Imf ≤_e Kerg and Img ≤_e C. We modify many famous theorems including exact sequences to one includes e-exact sequences like 3 × 3 lemma, four and five lemmas. Next, we prove that for torsion-free module M, the contravariant functor Hom(-, M) is left e-exact and the covariant functor M ⊗ - is right e-exact. Finally, we define e-projective module and characterize it. We show that the direct sum of R-modules is e-projective module if and only if each summand is e-projective.

• 호남수학학술지
• /
• 제29권2호
• /
• pp.289-297
• /
• 2007

In this paper, we show that BCI-algebras P and Q are injective if and only if its direct sum P $\oplus$ Q is injective. Moreover, we obtain the equivalent conditions for a p-semisimple BCI-algebra to be p-injective.