• Title/Summary/Keyword: subalgebra

Search Result 133, Processing Time 0.018 seconds

Full hereditary $C^{*}$-subalgebras of crossed products

  • Jeong, Ja A.
    • Bulletin of the Korean Mathematical Society
    • /
    • v.30 no.2
    • /
    • pp.193-199
    • /
    • 1993
  • A hereditary $C^{*}$-subalgebra B of a $C^{*}$-algebra A is said to be full if B is not contained in any proper closed two-sided ideal in A, so each hereditary $C^{*}$-subalgebra of a simple $C^{*}$-algebra is always full. It is well known that every $C^{*}$-algebra is strong Morita equivalent to its full hereditary $C^{*}$-subalgebra, but the strong Morita equivalence of a $C^{*}$-algebra A and its hereditary $C^{*}$-subalgebra B does not imply the fullness of B, ingeneral. We present the following lemma for our computational convenience in the course of the proof of the main theorem. Note that $L_{B}$, $L_{B}$$^{*}$ and $L_{B}$ $L_{B}$$^{*}$ are all .alpha.-invariant whenever B is .alpha.-invariant under the action .alpha. of G.a. of G.a. of G.a. of G.f G.

  • PDF

N-SUBALGEBRAS OF TYPE (∈, ∈ ∨ q) BASED ON POINT N-STRUCTURES IN BCK/BCI-ALGEBRAS

  • Lee, Kyoung-Ja;Jun, Young-Bae;Zhang, Xiaohong
    • Communications of the Korean Mathematical Society
    • /
    • v.27 no.3
    • /
    • pp.431-439
    • /
    • 2012
  • Characterizations of $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) are provided. The notion of $\mathcal{N}$-subalgebras of type ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) is introduced, and its characterizations are discussed. Conditions for an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) (resp. ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) to be an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}$) are considered.

Quasi-Valuation Maps on BCK/BCI-Algebras

  • SONG, SEOK-ZUN;ROH, EUN HWAN;JUN, YOUNG BAE
    • Kyungpook Mathematical Journal
    • /
    • v.55 no.4
    • /
    • pp.859-870
    • /
    • 2015
  • The notion of quasi-valuation maps based on a subalgebra and an ideal in BCK/BCI-algebras is introduced, and then several properties are investigated. Relations between a quasi-valuation map based on a subalgebra and a quasi-valuation map based on an ideal is established. In a BCI-algebra, a condition for a quasi-valuation map based on an ideal to be a quasi-valuation map based on a subalgebra is provided, and conditions for a real-valued function on a BCK/BCI-algebra to be a quasi-valuation map based on an ideal are discussed. Using the notion of a quasi-valuation map based on an ideal, (pseudo) metric spaces are constructed, and we show that the binary operation * in BCK-algebras is uniformly continuous.

T-FUZZY CIRCLED SUBALGEBRAS OF BCK-ALGEBRAS

  • Kim, Kyung-Ho;Jun, Young-Bae
    • Journal of applied mathematics & informatics
    • /
    • v.7 no.2
    • /
    • pp.685-692
    • /
    • 2000
  • We introduce the notion of T-fuzzy circled subalgebras, and obtain some related results.

A NOTE ON WEAKLY PATH-CONNECTED ORTHOMODULAR LATTICES

  • Park, Eun-Soon
    • Communications of the Korean Mathematical Society
    • /
    • v.12 no.3
    • /
    • pp.513-519
    • /
    • 1997
  • We show that each orthomodular lattice containing only atomic nonpath-connected blocks is a full subalgebra of an irreducible path-connected orthomodular lattice and there is a path-connected orthomodualr lattice L containing a weakly path-connected full subalgebra C(x) for some element x in L.

  • PDF

BIPOLAR FUZZY TRANSLATIONS IN BCK/BCI-ALGEBRAS

  • Jun, Young Bae;Kim, Hee Sik;Lee, Kyoung Ja
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.22 no.3
    • /
    • pp.399-408
    • /
    • 2009
  • A bipolar fuzzy translation and a bipolar fuzzy S-extension of a bipolar fuzzy subalgebra in a BCK/BCI-algebra are introduced, and related properties are investigated.

  • PDF

APPLICATIONS OF COUPLED N-STRUCTURES IN BH-ALGEBRAS

  • Seo, Min Jeong;Ahn, Sun Shin
    • Honam Mathematical Journal
    • /
    • v.34 no.4
    • /
    • pp.585-596
    • /
    • 2012
  • The notions of a $\mathcal{N}$-subalgebra, a (strong) $\mathcal{N}$-ideal of BH-algebras are introduced, and related properties are investigated. Characterizations of a coupled $\mathcal{N}$-subalgebra and a coupled (strong) $\mathcal{N}$-ideals of BH-algebras are given. Relations among a coupled $\mathcal{N}$-subalgebra, a coupled $\mathcal{N}$-ideal and a coupled strong $\mathcal{N}$ of BH-algebras are discussed.

NORMAL BCI/BCK-ALGEBRAS

  • Meng, Jie;Wei, Shi-Ming;Jun, Young-Bae
    • Communications of the Korean Mathematical Society
    • /
    • v.9 no.2
    • /
    • pp.265-270
    • /
    • 1994
  • In 1966, Iseki [2] introduced the notion of BCI-algebras which is a generalization of BCK-algebras. Lei and Xi [3] discussed a new class of BCI-algebra, which is called a p-semisimple BCI-algebra. For p-semisimple BCI-algebras, a subalgebra is an ideal. But a subalgebra of an arbitrary BCI/BCK-algebra is not necessarily an ideal. In this note, a BCI/BCK-algebra that every subalgebra is an ideal is called a normal BCI/BCK-algebra, and we give characterizations of normal BCI/BCK-algebras. Moreover we give a positive answer to the problem which is posed in [4].(omitted)

  • PDF

COUPLED N-STRUCTURES APPLIED TO IDEALS IN d-ALGEBRAS

  • Ahn, Sun Shin;Ko, Jung Mi
    • Communications of the Korean Mathematical Society
    • /
    • v.28 no.4
    • /
    • pp.709-721
    • /
    • 2013
  • The notions of coupled N-subalgebra, coupled (positive implicative) N-ideals of $d$-algebras are introduced, and related properties are investigated. Characterizations of a coupled $\mathcal{N}$-subalgebra and a coupled (positive implicative) $\mathcal{N}$-ideals of $d$-algebras are given. Relations among a coupled $\mathcal{N}$-subalgebra, a coupled $\mathcal{N}$-ideal and a coupled positive implicative $\mathcal{N}$-ideal of $d$-algebras are discussed.