• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.703-706
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• 2013

Let R be a commutative noetherian algebra and let ${\delta}$ be a nonzero derivation. Here we determine the prime ideals of the skew polynomial algebra R[z;${\delta}$] and the Poisson prime ideals of R[z;${\delta}$]p.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.579-591
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• 2015

Properties of prime filters are studied in BE-algebras as well as in commutative BE-algebras. An equivalent condition is derived for a BE-algebra to become a totally ordered set. A condition L is introduced in a commutative BE-algebra in ordered to study some more properties of prime filters in commutative BE-algebras. A set of equivalent conditions is derived for a commutative BE-algebra to become a chain. Some topological properties of the space of all prime filters of BE-algebras are studied.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.385-402
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• 2015

In this paper we study the (good) semi-prime closure operations on ideals of a BCK-algebra, lower BCK-semilattice, Noetherian BCK-algebra and meet quotient ideal and then we give several theorems that make different (good) semi-prime closure operations. Moreover by given some examples we show that the given different notions are independent together, for instance there is a semi-prime closure operation, which is not a good semi-prime. Finally by given the notion of "$c_f$-Max X", we prove that every member of "$c_f$-Max X" is a prime ideal. Also we conclude some more related results.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.269-276
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• 2015

We investigate the Hopf algebra conjugation, ${\chi}$, of the mod 2 Steenrod algebra, $\mathcal{A}_2$, in terms of the Hopf algebra conjugation, ${\chi}^{\prime}$, of the mod 2 Leibniz-Hopf algebra. We also investigate the fixed points of $\mathcal{A}_2$ under ${\chi}$ and their relationship to the invariants under ${\chi}^{\prime}$.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.15-21
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• 1999

In this paper, we introduce the notion of anti fuzzy prime ideals in a commutative BCK-algebra and obtain some properties of it.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.289-297
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• 2010

By using as main tool the theory of prime submodules this article is devoted to describing the structure of the minimal prime ideals of the equidimensional symmetric algebra of a finitely generated module.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.187-191
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• 1993

In this note we prove the following result: Let A be a complex Banach *-algebra with continuous involution and let B be an $A^{*}$-algebra./T(A) = B. Then T is continuous (Theorem 2). From above theorem some others results of special interest and some well-known results follow. (Corollaries 3,4,5,6 and 7). We close this note with some generalizations and some remarks (Theorems 8.9.10 and question). Throughout this note we consider only complex algebras. Let A and B be complex algebras. A linear mapping T from A into B is called jordan homomorphism if T( $x^{1}$) = (Tx)$^{2}$ for all x in A. A linear mapping T : A .rarw. B is called spectrally-contractive mapping if .rho.(Tx).leq..rho.(x) for all x in A, where .rho.(x) denotes spectral radius of element x. Any homomorphism algebra is a spectrally-contractive mapping. If A and B are *-algebras, then a homomorphism T : A.rarw.B is called *-homomorphism if (Th)$^{*}$=Th for all self-adjoint element h in A. Recall that a Banach *-algebras is a complex Banach algebra with an involution *. An $A^{*}$-algebra A is a Banach *-algebra having anauxiliary norm vertical bar . vertical bar which satisfies $B^{*}$-condition vertical bar $x^{*}$x vertical bar = vertical bar x vertical ba $r^{2}$(x in A). A Banach *-algebra whose norm is an algebra $B^{*}$-norm is called $B^{*}$-algebra. The *-semi-simple Banach *-algebras and the semi-simple hermitian Banach *-algebras are $A^{*}$-algebras. Also, $A^{*}$-algebras include $B^{*}$-algebras ( $C^{*}$-algebras). Recall that a semi-prime algebra is an algebra without nilpotents two-sided ideals non-zero. The class of semi-prime algebras includes the class of semi-prime algebras and the class of prime algebras. For all concepts and basic facts about Banach algebras we refer to [2] and [8].].er to [2] and [8].].

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.51-62
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• 2015

Pseudo-ŁBCK-algebras are commutative pseudo-BCK-algebras with relative cancellation property. In the paper, we introduce fuzzy prime ideals in pseudo-ŁBCK-algebras and investigate some of their properties. We also give various characterizations of prime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo-ŁBCKalgebra to be a pseudo-ŁBCK-chain.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.859-869
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• 1997

It is shown that for $A_{k, m}$ a k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1$ such that no non-trivial matrix algebra can be factored out of $A_{k, m}$ and $A_{k, m} \otimes M_l(C)$ has a non-trivial bundle structure for any positive integer l, we construct an $A_{k, m^-} C(S^{2n - 1} \times S^1) \otimes M_k(C)$-equivalence bimodule to show that every k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1)$. Moreover, we prove that the tensor product of the k-homogeneous $C^*$-algebra $A_{k, m}$ with a UHF-algebra of type $p^\infty$ has the tribial bundle structure if and only if the set of prime factors of k is a subset of the set of prime factors of pp.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.653-660
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• 2008

In this paper, we consider the fuzzification of prime filters in Lattice Implication Algebras (briefly, LIAs), and introduce the concepts of fuzzy prime filters (briefly, FP-filters), and we also studied the properties of FP-filters. Finally, we investigate the properties of fuzzy prime dual filters (briefly, FPD-filters) in LIA, and the relations of them are investigated.