Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by $V_{b}$ the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type $τ_{b}: {+,·,´} → N$, where $τ_{b}(+) = τ_{b}(·) = 2$ and $τ_{b}(´) = 1$. In this paper we characterize the lattice $ℒ(B_{b})$ of all subvarieties of the biregularization of the variety B.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
Let τ be a type of algebras without nullary fundamental operation symbols. We call an identity φ ≈ ψ of type τ clone compatible if φ and ψ are the same variable or the sets of fundamental operation symbols in φ and ψ are nonempty and identical. For a variety 𝓥 of type τ we denote by $𝓥^{c}$ the variety of type τ defined by all clone compatible identities from Id(𝓥). We call $𝓥^{c}$ the clone extension of 𝓥. In this paper we describe algebras and minimal generics of all subvarieties of $𝓑^{c}$, where 𝓑 is the variety of Boolean algebras.
3
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW