• East Asian mathematical journal
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• v.19 no.2
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• pp.233-240
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• 2003

Xie and Wu introduced an m-system in a po-semigroup. Kehayopulu gave characterizations of weakly prime ideals of po-semigroups and Lee and Kwon add two characterizations for weakly prime ideals. In this paper, we give a characterization of weakly prime ideals and a characterization of weakly semi-prime ideals in po-semigroups using m-system and n-system, respectively

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.117-122
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• 2010

In this paper, we introduce the concepts of 1-prime ideals and 2-prime ideals in semirings. We have also introduced $m_1$-system and $m_2$-system in semiring. We have shown that if Q is an ideal in the semiring R and if M is an $m_2$-system of R such that $\overline{Q}{\bigcap}M={\emptyset}$ then there exists as 2-prime ideal P of R such that Q $\subseteq$ P with $P{\bigcap}M={\emptyset}$.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.82-100
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• 2024

The main objective of the study is to introduce ideals of Sheffer stroke Hilbert algebras by means of fuzzy points, and investigate some properties. The process of making (fuzzy) ideals and fuzzy deductive systems through the fuzzy points of Sheffer stroke Hilbert algebras is illustrated, and the (fuzzy) ideals and the fuzzy deductive systems are characterized. Certain sets are defined by virtue of a fuzzy set, and the conditions under which these sets can be ideals are revealed. The union and intersection of two fuzzy ideals are analyzed, and the relationships between aforementioned structures of Sheffer stroke Hilbert algebras are built.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1271-1290
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• 2013

Let M be a fixed left R-module. For a left R-module X, we introduce the notion of M-prime (resp. M-semiprime) submodule of X such that in the case M=R, it coincides with prime (resp. semiprime) submodule of X. Other concepts encountered in the general theory are M-$m$-system sets, M-$n$-system sets, M-prime radical and M-Baer's lower nilradical of modules. Relationships between these concepts and basic properties are established. In particular, we identify certain submodules of M, called "primeM-ideals", that play a role analogous to that of prime (two-sided) ideals in the ring R. Using this definition, we show that if M satisfies condition H (defined later) and $Hom_R(M,X){\neq}0$ for all modules X in the category ${\sigma}[M]$, then there is a one-to-one correspondence between isomorphism classes of indecomposable M-injective modules in ${\sigma}[M]$ and prime M-ideals of M. Also, we investigate the prime M-ideals, M-prime submodules and M-prime radical of Artinian modules.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.863-872
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• 2007

Let D be an integral domain with quotient field K, A a nonempty set of height-one maximal t-ideals of D, F$({\Lambda})={I{\subseteq}D|I$ is an ideal of D such that $I{\subseteq}P$ for all $P{\in}A}$, and $D_F({\Lambda})={x{\in}K|xA{\subseteq}D$ for some $A{\in}F({\Lambda})}$. In this paper, we prove that if each $P{\in}A$ is the radical of a finite type v-ideal (resp., a principal ideal), then $D_{F({\Lambda})}$ is a weakly Krull domain (resp., generalized weakly factorial domain) if and only if the intersection $D_{F({\Lambda})}={\cap}_{P{\in}A}D_P$ has finite character, if and only if $F({\Lambda})$ is a t-splitting set of ideals, if and only if $F({\Lambda})$ is v-finite.

• Communications of the Korean Mathematical Society
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• v.23 no.1
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• pp.1-10
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• 2008

Conditions for an ideal to be irreducible are provided. The notion of an order system in a subtraction algebra is introduced, and related properties are investigated. Relations between ideals and order systems are given. The concept of a fixed map in a subtraction algebra is discussed, and related properties are investigated.

• East Asian mathematical journal
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• v.28 no.3
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• pp.281-285
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• 2012

In this paper, the concept of *-prime ideals in non-associative near-rings is introduced and then will be studied. For this purpose, first we introduce the notions of *-operation, *-prime ideal and *-system in a near-ring. Next, we will define the *-sequence, *-strongly nilpotent *-prime radical of near-rings, and then obtain some characterizations of *-prime ideal and *-prime radical $r_s$(I) of an ideal I of near-ring N.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.689-698
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• 2021

In this paper, we show some results on the artinianness of local cohomology modules with respect to a system of ideals. If M is a 𝚽-minimax ZD-module, then H^{dim M}_𝚽(M)/𝖆H^{dim M}_𝚽(M) is artinian for all 𝖆 ∈ 𝚽. Moreover, if M is a 𝚽-minimax ZD-module, t is a non-negative integer and Hⁱ_𝚽(M) is minimax for all i > t, then Hⁱ_𝚽(M) is artinian for all i > t.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.559-573
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• 2006

In this Paper three different types of fuzzy Prime ideals are introduced. Condition is obtained for a fuzzy 2-prime ideal will have two elements in its range. It has been shown that A is fuzzy 2-prime ideal of the semiring R if and only if 1-A is a fuzzy $m_2-system$ in R.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.449-458
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• 2002

We shall give a gereralization for a new right congruence induced by right congruences on S and right ideals of S and discuss the radicals associated with automata. Also we shall discuss the relationship between the collection of all right ideals in S and the collection of all right congruences on S.