• Title/Summary/Keyword: subalgebra

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Structures of Pseudo Ideal and Pseudo Atom in a Pseudo Q-Algebra

  • Jun, Young Bae;Kim, Hee Sik;Ahn, Sun Shin
    • Kyungpook Mathematical Journal
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    • v.56 no.1
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    • pp.95-106
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    • 2016
  • As a generalization of Q-algebra, the notion of pseudo Q-algebra is introduced, and some of their properties are investigated. The notions of pseudo subalgebra, pseudo ideal, and pseudo atom in a pseudo Q-algebra are introduced. Characterizations of their properties are provided.

FUZZY ABYSMS OF HILBERT ALGEBRAS

  • Jun, Young-Bae;Lee, Kyoung-Ja;Park, Chul-Hwan
    • The Pure and Applied Mathematics
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    • v.15 no.4
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    • pp.377-385
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    • 2008
  • The notion of fuzzy abysms in Hilbert algebras is introduced, and several properties are investigated. Relations between fuzzy subalgebra, fuzzy deductive systems, and fuzzy abysms are considered.

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COMPUTATION OF WEDDERBURN DECOMPOSITION OF GROUPS ALGEBRAS FROM THEIR SUBALGEBRA

  • Mittal, Gaurav;Sharma, Rajendra Kumar
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.3
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    • pp.781-787
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    • 2022
  • In this paper, we show that under certain conditions the Wedderburn decomposition of a finite semisimple group algebra 𝔽qG can be deduced from a subalgebra 𝔽q(G/H) of factor group G/H of G, where H is a normal subgroup of G of prime order P. Here, we assume that q = pr for some prime p and the center of each Wedderburn component of 𝔽qG is the coefficient field 𝔽q.

PROJECTIVE LIMIT OF A SEQUENCE OF BANACH FUNCTION ALGEBRAS AS A FRECHET FUNCTION ALGEBRA

  • Sady. F.
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.2
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    • pp.259-267
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    • 2002
  • Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.

PATH-CONNECTED AND NON PATH-CONNECTED ORTHOMODULAR LATTICES

  • Park, Eun-Soon;Song, Won-Hee
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.845-856
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    • 2009
  • A block of an orthomodular lattice L is a maximal Boolean subalgebra of L. A site is a subalgebra of an orthomodular lattice L of the form S = A $\cap$ B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if |A $\cap$ B| < $\infty$ for all distinct blocks A, B of L. We prove that there exists a weakly path-connected orthomodular lattice with finite sites which is not path-connected and if L is an orthomodular lattice such that the height of the join-semilattice [ComL]$\vee$ generated by the commutators of L is finite, then L is pathconnected.

SOFT BCC-ALGEBRAS

  • Jun, Young-Bae;Lee, Kyoung-Ja;Ozturk, Mehmet Ali
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1293-1305
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    • 2009
  • Molodtsov [D. Molodtsov, Soft set theory First results, Comput. Math. Appl. 37 (1999) 19-31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of BCC-algebras. The notion of (trivial, whole) soft BCC-algebras and soft BCC-subalgebras are introduced, and several examples are provided. Relations between a fuzzy subalgebra and a soft BCC-algebra are given, and the characterization of soft BCC-algebras is established.

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MAXIMALITY OF THE ANALYTIC SUBALGEBRAS OF C*-ALGEBRAS WITH FLOWS

  • Kishimoto, Akitaka
    • Journal of the Korean Mathematical Society
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    • v.50 no.6
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    • pp.1333-1348
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    • 2013
  • Given a faithful flow ${\alpha}$ on a $C^*$-algebra A, when A is ${\alpha}$-simple we will show that the closed subalgebra of A consisting of elements with non-negative Arveson spectra is maximal if and only if the crossed product of A by ${\alpha}$ is simple. We will also show how the general case can be reduced to the ${\alpha}$-simple case, which roughly says that any flow with the above maximality is an extension of a trivial flow by a flow of the above type in the ${\alpha}$-simple case. We also propose a condition of essential maximality for such closed subalgebras.

FILTER SPACES AND BASICALLY DISCONNECTED COVERS

  • Jeon, Young Ju;Kim, ChangIl
    • The Pure and Applied Mathematics
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    • v.21 no.2
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    • pp.113-120
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    • 2014
  • In this paper, we first show that for any space X, there is a ${\sigma}$-complete Boolean subalgebra of $\mathcal{R}$(X) and that the subspace {${\alpha}{\mid}{\alpha}$ is a fixed ${\sigma}Z(X)^{\sharp}$-ultrafilter} of the Stone-space $S(Z({\Lambda}_X)^{\sharp})$ is the minimal basically disconnected cover of X. Using this, we will show that for any countably locally weakly Lindel$\ddot{o}$f space X, the set {$M{\mid}M$ is a ${\sigma}$-complete Boolean subalgebra of $\mathcal{R}$(X) containing $Z(X)^{\sharp}$ and $s_M^{-1}(X)$ is basically disconnected}, when partially ordered by inclusion, becomes a complete lattice.