• The Pure and Applied Mathematics
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• v.21 no.2
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• pp.105-112
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• 2014

The notion of intersection-soft ideal of CI-algebras is introduced, and related properties are investigated. A characterization of an intersection-soft ideal is provided, and a new intersection-soft ideal from the old one is established.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.43-54
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• 2014

The notions of cubic subalgebras and cubic filters in CI-algebras are introduced, and related properties are investigated. Characterizations of cubic subalgebras are considered. Conditions for a cubic set to be a cubic filter are provided.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.143-153
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• 2014

The notion of double-framed soft filters of a CI-algebra is introduced, and related properties are investigated. Further characterization of a double-framed soft filter is considered, and conditions for a double-framed soft set to be a double-framed soft filter are provided. Finally a new double-framed soft filter from old one is established.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.57-64
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• 2014

It is known that the class of CI-algebras is a generalization of the class of BE-algebras [5]. Recently, K. H. Kim introduced the notion of a CS-algebra [4]. In this paper we discuss a closed deductive system of a CS-algebra, and we find some fundamental properties. Moreover, we study a CS-algebra homomorphism and a congruence relation.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.489-496
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• 2012

In this paper, we introduce the notions of Smarandache weak BE-algebra, Q-Smarandache filters and Q-Smarandache ideals. We show that a nonempty subset F of a BE-algebra X is a Q-Smarandache filter if and only if $A(x,y){\subseteq}F$, which A($x,y$) is a Q-Smarandache upper set The relationship between these notions are stated and proved.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.297-307
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• 2014

The present paper gives the notion of a derivation on a CI-algebra X and investigates related properties. We define a set $Fix_d(X)$ by $Fix_d(X)=\{x{\in}X{\mid}d(x)=x\}$, where d is a derivation on a CI-algebra X. We show that $Fix_d(X)$ is a subalgebra of X. Also, we prove some one-to-one and onto derivation theorems. Moreover, we study a regular derivation on a CI-algebra and an isotone derivation on a transitive CI-algebra.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1379-1410
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• 2017

Kang and Ko introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4. Let $R=k[w_0,\;w_1,\;w_2,\;{\ldots},\;w_m]$ be the polynomial ring over an algebraically closed field k with indetermiantes $w_l$ and deg $w_l=1$, and $I_i$ a homogeneous perfect ideal of grade 3 with type $t_i$ defined by a skew-symmetrizable matrix $G_i(1{\leq}t_i{\leq}4)$. We show that for m = 2 the Hilbert function of the zero dimensional standard k-algebra $R/I_i$ is determined by CI-sequences and a Gorenstein sequence. As an application of this result we show that for i = 1, 2, 3 and for m = 3 a Gorenstein sequence $h(R/H_i)=(1,\;4,\;h_2,\;{\ldots},\;h_s)$ is unimodal, where $H_i$ is the sum of homogeneous perfect ideals $I_i$ and $J_i$ which are geometrically linked by a homogeneous regular sequence z in $I_i{\cap}J_i$.