Our work proposes a new paradigm for the study of various classes of cancellative residuated lattices by viewing these structures as lattice-ordered groups with a suitable operator (a conucleus). One consequence of our approach is the categorical equivalence between the variety of cancellative commutative residuated lattices and the category of abelian lattice-ordered groups endowed with a conu...

Let K be any unital commutative Q-algebra and z = (z1, · · · , zn) commutative or noncommutative free variables. Let t be a formal parameter which commutes with z and elements of K. We denote uniformly by K〈〈z〉〉 and K[[t]]〈〈z〉〉 the formal power series algebras of z over K and K[[t]], respectively. For any α ≥ 1, let D〈〈z〉〉 be the unital algebra generated by the differential operators of K〈〈z〉〉 ...

Let A be a Banach algebra. We call a pair (G,A) a Gelfand theory for A if the following axioms are satisfied: (G 1) A is a C∗-algebra, and G : A → A is a homomorphism; (G 2) the assignment L 7→ G−1(L) is a bijection between the sets of maximal modular left ideals of A and A, respectively; (G 3) for each maximal modular left ideal L of A, the linear map GL : A/G−1(L) → A/L induced by G has dense...

The purpose of this paper is to give the algebraic topological background for elliptic cohomology theory and to pose some number theoretic problems suggested by these concepts. Algebraic topologists study functors from the category of spaces to various algebraic categories. In particular there are functors to the category of graded rings called multiplicative generalized cohomology theories. (A...

The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring elementary, i.e. we can express with elementary ones in unique way. does not extend directly to semirings, but do have analogous results for some special example, the tropical, extended and supertropical semirings. These all fall into larger class upper-bound In this...

The category of Hopf monoids over an arbitrary symmetric monoidal category as well as its subcategories of commutative and cocommutative objects respectively are studied, where attention is paid in particular to the following questions: (a) When are the canonical forgetful functors of these categories into the categories of monoids and comonoids respectively part of an adjunction? (b) When are ...

Some simple Lie superalgebras, specific of characteristic 3, defined by S. Bouarroudj and D. Leites [BL06], will be related to the simple alternative and commutative superalgebras discovered by I.P. Shestakov [She97]. Throughout the paper, the ground field k will always be assumed to be of characteristic 6= 2. 1. Tits construction In 1966 [Tit66], Tits gave a unified construction of the excepti...

Let IK be a complete ultrametric field and let A unital commutative Banach IK-algebra. Suppose that the multiplicative spectrum admits partition in two open closed subsets. Then there exist unique idempotents u, v ϵ such ϕ (u) = 1, (v) 0 ∀ U, 1 V . is algebraically closed. If an element x has empty annulus r < |ξ − a| s its sp(x), then 1; whenever (x a) ≤ 0; ≥ s.

The Alesker product turns the space of smooth translation-invariant valuations on convex bodies into a commutative associative unital algebra, satisfying Poincaré duality and hard Lefschetz theorem. In this article, version Hodge-Riemann relations for algebra is conjectured, conjecture proved in two particular situations: even valuations, 1-homogeneous valuations. latter result then used to ded...