Some Characterizations of Nil Ideals in BCI—algebras

51.IntrodcutionIn[1j,thenotionsofnilidealinBCI-algebrasandinlBCI-algebrawereintreduced.WeshowthatnilBCI-algebraisageneralizationofassociativeandquasi-associativeBCIalgebra([2J,[3j).lnthispaper,somecharacterizationsofnilidealsinBCI-algebraswereproved.Moreover,theBCI-algebrassatifyingO*x.=xwerediscussedandvariousproPertieswereproved.Werecallsomedefinitionsande1ementaryproperties.ThefollowingsaretrueinaBCI-al-gebra:(l)x o=x;(2)(x*y)*z=(x z) y;(3)x相似文献   

Fuzzy Strongly Implicative Ideals in BCI－Algebras(Ⅱ)

For the homomorphic image f(μ) and preimage f-1(υ) of fuzzy strongly implicative ideals μ and υ,respectively, we establish the chains of level strongly implicative ideals of f(μ) and f-1(υ),respectively. We construct a new fuzzy strongly implicative ideal from old. Finally,we consider the normality of a fuzzy strongly implicative ideal in a BCI-algebra.     

Some Properties of a Class Self—homomorphism of BCI—algebras

ＢｙａＢＣＩ－ａｌｇｅｂｒａｗｅｍｅａｎａｎａｌｇｅｂｒａ（Ｘ；，０）ｏｆｔｙｐｅ（２，０）ｓａｔｉｓｆｙｉｎｇｔｈｅａｘｉｏｍｓ：（１）（（ｘｙ）（ｘｚ））（ｚｙ）＝０；（２）（ｘ（ｘｙ））ｙ＝０；（３）ｘｘ＝０；（４）ｘｙ＝ｙｘ＝０ｘ＝ｙｆｏｒａｎｙｘ，ｙａｎｄｚｉｎＸ．ＦｏｒａｎｙＢＣＩ－ａｌｇｅｂｒａＸ，ｔｈｅｒｅｌａｔｉｏｎ≤ｄｅｆｉｎｅｄｂｙｘ≤ｙｉｆａｎｄｏｎｌｙｉｆｘｙ＝０ｉｓａｐａｒｔｉａｌｏｒｄｅｒｏｎＸ［１］．ＩｎａｎｙＢＣＩ－ａｌｇｅｂｒａＸ，…     

Ideals in Morita Rings and Morita Semigroups

We characterize the lattice of all ideals of a Morita ring （semigroup） when the corresponding pair of rings （semigroups） in the Morita context are Morita equivalent s-unital （like-unitv） rings （semigroups）.     

Centralinvariants of ρ-Lie algebras in Yetter-Drinfeldcategories

The central invariants of the derived ρ-Lie algebras in Yetter-Drinfeld categories are studied.     

Multiplier Ideals of General Line Arrangements in ℂ3

We consider the multiplier ideals of the ideal of a reduced union of lines through the origin in ?³. For general arrangements of lines, we calculate the multiplier ideals.     

Fuzzy Strongly Implicative Ideals in BCI-Algebras(Ⅱ)

§１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｏｎｃｅｐｔｏｆｆｕｚｙｓｅｔｓｗａｓｉｎｔｒｏｄｕｃｅｄｂｙＬ．Ａ．Ｚａｄｅｈ［８］．Ｓｉｎｃｅｔｈｅｎｔｈｅｓｅｉｄｅａｓｈａｖｅｂｅｅｎａｐｐｌｉｅｄｔｏｏｔｈｅｒａｌｇｅｂｒａｉｃｓｔｒｕｃｔｕｒｅｓｓｕｃ...     

Tubular algebras and affine Kac-Moody algebras

The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)1C/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)1C generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)1C generated by simple A-modules.     

The Pointwise Characterizations of Fuzzy Ideals and Fuzzy Prime Ideals

TheconceptofthefuzzysubgroupsintroducedinRosenfeld[l],wasappliedtogeneralizesomeofthebasicconceptsofalgebra.In[2,3,4]LuWangjindefinedfuzzysubringsandfuzzyideals,introducedtheoperationsonfuzzyidea1s.In[5]theautherdiscussedaboutthenatureoffuzzysubringsbythenestedsubring.Butthepointwisedefinitionsoffuzzysubgroupsandfuzzysubringsarerare.Inthispaper,theautherprogramsanddiscussesthefuzzysubrings,fuzzyidealsandfuzzyprimeidealsbyfuzzyPoints..5l.PreliminariesLetusrecallsomeconceptsoccurrjnginthe[2,3…     

Endomorphism algebras and Igusa–Todorov algebras

Let A be an Artin algebra. If $V\in \operatorname{mod} A$ such that the global dimension of  $\operatorname{End}_{A}V$ is at most 3, then for any ${M\in \operatorname{add}_{A}V}$ , both B and B ^op are 2-Igusa–Todorov algebras, where ${B=\operatorname{End}_{A}M}$ . Let ${P\in \operatorname{mod} A}$ be projective and ${B=\operatorname{End}_{A}P}$ such that the projective dimension of P as a right B-module is at most n(<∞). If A is an m-syzygy-finite algebra (resp. an m-Igusa–Todorov algebra), then B is an (m+n)-syzygy-finite algebra (resp. an (m+n)-Igusa–Todorov algebra); in particular, the finitistic dimension of B is finite in both cases. Some applications of these results are given.     

Piecewise-Koszul algebras

It is a small step toward the Koszul-type algebras.The piecewise-Koszul algebras are, in general,a new class of quadratic algebras but not the classical Koszul ones,simultaneously they agree with both the classical Koszul and higher Koszul algebras in special cases.We give a criteria theorem for a graded algebra A to be piecewise-Koszul in terms of its Yoneda-Ext algebra E(A),and show an A_∞-structure on E(A).Relations between Koszul algebras and piecewise-Koszul algebras are discussed.In particular,our results are related to the third question of Green-Marcos.     

Lie-admissible algebras and generalized witt algebras ∗

The symmetric group 𝔖_n+1 of degree n + 1 admits an n-dimensional irreducible Q𝔖_n-module V corresponding to the hook partition (2, 1^n?1). By the work of Craig and Plesken, we know that there are σ(n + 1) many isomorphism classes of Z𝔖_n+1-lattices which are rationally equivalent to V, where σ denotes the divisor counting function. In the present article, we explicitly compute the Solomon zeta function of these lattices. As an application we obtain the Solomon zeta function of the Z𝔖_n+1-lattice defined by the Specht basis.     

On Rough Intuitionistic Fuzzy Ideals（Filters） in Lattices

In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal（filter） which is a generalized intuitionistic fuzzy ideal（filter） of a lattice and study some related properties of such ideals（filters）.     

Cohen–Macaulay Auslander algebras of skewed-gentle algebras

For any skewed-gentle algebra, we characterize its indecomposable Gorenstein projective modules explicitly and describe its Cohen–Macaulay Auslander algebra. We prove that skewed-gentle algebras are always Gorenstein, which is independent of the characteristic of the ground field, and the Cohen–Macaulay Auslander algebras of skewed-gentle algebras are also skewed-gentle algebras.     

The Integral Closure of Ideals in ℂ{x,y}

Abstract

We give some techniques to determine the ideal K _I generated by the monomials x ^{k ₁} y ^{k ₂} belonging to the integral closure ī of an ideal I ? ?{x, y}. We also give a sufficient condition for a weighted homogeneous ideal I ? ?{x, y} to satisfy the relation ī = I + K _I .     

C~*-index of observable algebras in G-spin model

In two-dimensional lattice spin systems in which the spins take values in afinite group G,one can define a field algebra F which carries an action of a Hopf algebraD(G),the double algebra of G and moreover,an action of D(G;H),which is a subalgebraof D(G)determined by a subgroup H of G,so that F becomes a modular algebra.Theconcrete construction of D(G;H)-invariant subspace A_H in F is given.By constructingthe quasi-basis of conditional expectation γ_G of A_H onto A_G,the C~*-index of γ_G is exactlythe index of H in G.     

Δ20-categoricity in Boolean algebras and linear orderings

We characterize Δ₂⁰-categoricity in Boolean algebras and linear orderings under some extra effectiveness conditions. We begin with a study of the relativized notion in these structures.