In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary ...In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary case.展开更多
Let R be a commutative ring with 1≠ 0. A proper ideal I of R is a semiprimary ideal of R if whenever a, b ∈ R and a b ∈ I, we have a ∈ √I or b ∈√I; and I is a weakly semiprimary ideal of R if whenever a, b ∈ R...Let R be a commutative ring with 1≠ 0. A proper ideal I of R is a semiprimary ideal of R if whenever a, b ∈ R and a b ∈ I, we have a ∈ √I or b ∈√I; and I is a weakly semiprimary ideal of R if whenever a, b ∈ R and 0 ≠ ab ∈ √I, we have a ∈√I or b ∈ √I. In this paper, we introduce a new class of ideals that is closely related to the class of （weakly） semiprimary ideals. Let I（R） be the set of all ideals of R and let δ ： I（R） → I（R） be a function. Then δ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J I, we have L δ（L） and δ（J） δ（I）. Let δ be an expansion function of ideals of R. Then a proper ideal I of R is called a δ-semiprimary （weakly δ-semiprimary） ideal of R if ab ∈ I （0 ≠ ab ∈ I） implies a ∈ δ（I） or b∈ δ（I）. A number of results concerning weakly δ-semiprimary ideals and examples of weakly δ-semiprimary ideals are given.展开更多
In this paper, we show that every weakly a uniform topology （weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short） with which E is a first-countable, zero-dimensional, disconnect...In this paper, we show that every weakly a uniform topology （weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short） with which E is a first-countable, zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation ＋ of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation - of effect algebras and the operations A and V of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.展开更多
Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module...Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p.展开更多
Let R be a commutative ring with 1≠0.We introduce the concept of weakly 1-absorbing primary ideal,which is a generalization of 1-absorbing primary ideal.Aproperideal I of R is said tobeweakly1-absorbing primary if wh...Let R be a commutative ring with 1≠0.We introduce the concept of weakly 1-absorbing primary ideal,which is a generalization of 1-absorbing primary ideal.Aproperideal I of R is said tobeweakly1-absorbing primary if whenevernonunit elements a,b,c∈R and O≠abc∈I,we have ab∈I or c∈√I.A number of results concerning weakly 1-absorbing primary ideals are given,as well as examples of weakly 1-absorbing primary ideals.Furthermore,we give a corrected version of a result on 1-absorbing primary ideals of commutative rings.展开更多
文摘In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary case.
文摘Let R be a commutative ring with 1≠ 0. A proper ideal I of R is a semiprimary ideal of R if whenever a, b ∈ R and a b ∈ I, we have a ∈ √I or b ∈√I; and I is a weakly semiprimary ideal of R if whenever a, b ∈ R and 0 ≠ ab ∈ √I, we have a ∈√I or b ∈ √I. In this paper, we introduce a new class of ideals that is closely related to the class of （weakly） semiprimary ideals. Let I（R） be the set of all ideals of R and let δ ： I（R） → I（R） be a function. Then δ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J I, we have L δ（L） and δ（J） δ（I）. Let δ be an expansion function of ideals of R. Then a proper ideal I of R is called a δ-semiprimary （weakly δ-semiprimary） ideal of R if ab ∈ I （0 ≠ ab ∈ I） implies a ∈ δ（I） or b∈ δ（I）. A number of results concerning weakly δ-semiprimary ideals and examples of weakly δ-semiprimary ideals are given.
基金Supported by National Natural Science Foundation of China(Grant Nos.11401469 and 11171200)Shaanxi Province Natural Science Foundation(Grant No.2014JQ1032)
文摘In this paper, we show that every weakly a uniform topology （weakly algebraic ideal topology, algebraic ideal of an effect algebra E induces for short） with which E is a first-countable, zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation ＋ of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation - of effect algebras and the operations A and V of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.
基金This research is in part supported by a grant from IPM.
文摘Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p.
文摘Let R be a commutative ring with 1≠0.We introduce the concept of weakly 1-absorbing primary ideal,which is a generalization of 1-absorbing primary ideal.Aproperideal I of R is said tobeweakly1-absorbing primary if whenevernonunit elements a,b,c∈R and O≠abc∈I,we have ab∈I or c∈√I.A number of results concerning weakly 1-absorbing primary ideals are given,as well as examples of weakly 1-absorbing primary ideals.Furthermore,we give a corrected version of a result on 1-absorbing primary ideals of commutative rings.
