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.1080/00927879408825152 . [2] Panaite , F. , Oystaeyen Van , F. 2007 A structure theorem for quasi-Hopf comodule algebras Proc. Amer. Math. Soc. 135 1669 – 1677 10.1090/S0002-9939-07-08712-6 . [3
Abstract
The paper is concerned with endomorphism algebras for weak Doi-Hopf modules. Under the condition “weak Hopf-Galois extensions”, we present the structure theorem of endomorphism algebras for weak Doi-Hopf modules, which extends Theorem 3.2 given by Schneider in [1]. As applications of the structure theorem, we obtain the Kreimer-Takeuchi theorem (see Theorem 1.7 in [2]) and the Nikshych duality theorem (see Theorem 3.3 in [3]) in the case of weak Hopf algebras, respectively.
We deal with structure theory of Ambrose algebras, getting structure theorems, analogous to the classical ones of Wedderburn.
Abstract
The concept of `adjunct' operation of two lattices with respect to a pair of elements is introduced. A structure theorem namely, `A finite lattice is dismantlable if and only if it is an adjunct of chains' is obtained. Further it is established that for any adjunct representation of a dismantlable lattice the number of chains as well as the number of times a pair of elements occurs remains the same. If a dismantlable lattice L has n elements and n+k edges then it is proved that the number of irreducible elements of L lies between n-2k-2 and n-2. These results are used to enumerate the class of lattices with exactly two reducible elements, the class of lattices with n elements and upto n+1 edges, and their subclasses of distributive lattices and modular lattices.
Abstract
In this paper, we introduce comatrix group corings and define the generalized Galois group corings. Then we give the generalized Galois group coring Structure Theorem.
References [1] Lev , V. 1997 Addendum to “Structure theorem for multiple addition” J. Number Theory 65
Abstract
An orthogroup is a completely regular semigroup whose idempotents form a subsemigroup. For any semigroup S and a, x ∈ S, x is an associate of a if a = axa. A subgroup G of S is an associate subgroup of S if for every element a of S, G contains exactly one associate of a. An idempotent e of S is medial if for any element s of S which is a product of idempotents holds s = ses. We characterize orthogroups with an associate subgroup in several ways using the structural description of orthogroups as a semilattice of rectangular groups. Using the Blyth-Martins structure theorem for semigroups with an associate sub-group whose identity element is medial, we provide multiple characterizations of orthogroups, and some related semigroups, with an associate subgroup.
