the aim of this paper is to extend results established by h. onoand t. kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. the main theorem states that a residuatedlattice a is directly indecomposable if and only if its boolean center b(a)is {0, 1}. we also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...

In this paper, we study residuated lattices in order to give new characterizations for dense, regular and Boolean elements in residuated lattices and investigate special residuated lattices in order to obtain new characterizations for the directly indecomposable subvariety of Stonean residuated lattices. Free algebra in varieties of Stonean residuated lattices is constructed. We introduce in re...

The aim of this paper is to extend results established by H. Onoand T. Kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. The main theorem states that a residuatedlattice A is directly indecomposable if and only if its Boolean center B(A)is {0, 1}. We also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...

First a problem of Ralph McKenzie is answered by proving that in a nitely directly representable variety every directly indecomposable algebra must be nite. Then we show that there is no local proof of the fundamental theorem of Abelian algebras nor of H. P. Gumm's permutability results. This part may also be of interest for those investigating non-modular Abelian algebras. Finally we provide a...

The aim of this paper is double. From one side we survey the knowledge we have acquired these last ten years about the lattice of all λ-theories (= equational extensions of untyped λ-calculus) and the models of lambda calculus via universal algebra. This includes positive or negative answers to several questions raised in these years as well as several independent results, the state of the art ...

this paper is the first of a two part series. in this paper, we first prove that the variety of dually quasi-de morgan stone semi-heyting algebras of level 1 satisfies the strongly blended $lor$-de morgan law introduced in cite{sa12}. then, using this result and the results of cite{sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...

this paper is the second of a two part series. in this part, we prove, using the description of simples obtained in part i, that the variety $mathbf{rdqdstsh_1}$ of regular dually quasi-de morgan stone semi-heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{rdqdstsh_1}$-chains and the variety of dually quasi-de morgan boolean semi-heyting algebras--...

Let p be an odd prime. In this paper we study the relationship between degeneracy and decomposability in abelian crossed products. In particular we construct an indecomposable abelian crossed product division algebra of exponent p and index p. The algebra we construct is generic in the sense of [AS78] and has the property that its underlying abelian crossed product is a decomposable division al...

In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.

In this paper, we prove that every Pre A∗-algebra A with 1 is isomorphic to the Pre A∗-algebra of all global sections of a sheaf of indecomposable Pre A∗-algebra over Boolean space and that sheaf of indecomposable Pre A∗-algebra with 1 over Boolean space is isomorphic to the sheaf obtained from the Pre A∗-algebra of all sections of the sheaf. Copyright c © 2011 Yang’s Scientific Research Instit...