Let S be a simplicial affine semigroup of dimension r and R=K[[S]] be the semigroup ring assigned to S, where K is a field. Then R is a Noetherian ring of krull dimension r. When r=1, S is a numerical semigroup whose assigned semigroup ring is a one dimensional Cohen-Ma More
Let S be a simplicial affine semigroup of dimension r and R=K[[S]] be the semigroup ring assigned to S, where K is a field. Then R is a Noetherian ring of krull dimension r. When r=1, S is a numerical semigroup whose assigned semigroup ring is a one dimensional Cohen-Macaulay ring. In this case, all each set of S is a finite set, and the number of its maximal elements with respect to the natural relation, is equal to the type of R. But in general, when r>1, the Apery sets of S are not necessarily finite. In this paper, we introduce r Apery sets of S whose intersection is a finite set and determines the type and the canonical module of R. This set coincides with an Apery set, when r=1. In particular, we extend the known facts about canonical module of numerical semigroups to all Cohen-Macaulay simplicial affine semigroups.
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T‎he commutativity‎ degree of a finite non-commutative semigroup S is defined to be the probability‎ of choosing a pair (x,y) of the elements of S such that x commutes with y‎. Obviously if S is a abelian semigroup, then commutativity degree of S is 1. I More
T‎he commutativity‎ degree of a finite non-commutative semigroup S is defined to be the probability‎ of choosing a pair (x,y) of the elements of S such that x commutes with y‎. Obviously if S is a abelian semigroup, then commutativity degree of S is 1. In this study, we consider semigroups are non-commutative and finite. ‎For a given positive integer n=p^α q^β where p and q are primes (2≤p
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Abstract.The theory of α- resolvent families was developed as a generalization of the classical theory of strongly continuous semigroups and cosine operator families, to study the fractional evolution equations with Caputo derivative of order α. An important More
Abstract.The theory of α- resolvent families was developed as a generalization of the classical theory of strongly continuous semigroups and cosine operator families, to study the fractional evolution equations with Caputo derivative of order α. An important problem in semigroup theory and also for cosine operator families is to discuss different type of boundedness (in terms of their generator) for these families. In this paper, we study polynomially bounded α- resolvent families. We impose conditions on the resolvent of a closed and densely defined linear operator to be the generator of an α-resolvent family. We also show that these conditions are necessary in the case of Hilbert spaces. This generalizes the result by T. Eisner on polynomially bounded semigroups. Moreover, since α- resolvent families describe the solutions to fractional evolution equations, with this generation result, we discuss the existence and stability of solutions to these problems at the same time.
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In this paper, approximately amenable modulo an ideal of Banach algebras, approximatelyamenable modulo an ideal of second dual of Banach algebras are investigated. Also, using theobtained results, it is shown that ()⋆⋆ is approximately amenable modulo ⋆⋆ if an More
In this paper, approximately amenable modulo an ideal of Banach algebras, approximatelyamenable modulo an ideal of second dual of Banach algebras are investigated. Also, using theobtained results, it is shown that ()⋆⋆ is approximately amenable modulo ⋆⋆ if and onlyif / is finite where is the induced ideal for the least group congruence on S.
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In this paper, we introduce the new concept of biprojectivity of a Banach algebra modulo an ideal, as a generalization of this notion in the classical case. By using it , we obtain some necessary and sufficient conditions for contractibility of Banach algebras modulo an More
In this paper, we introduce the new concept of biprojectivity of a Banach algebra modulo an ideal, as a generalization of this notion in the classical case. By using it , we obtain some necessary and sufficient conditions for contractibility of Banach algebras modulo an ideal. In particular we characterize the contractibility of quotient Banach algebras. Also we study the relationship between the biprojectivity modulo an ideal of a Banach algebra and the biprojectivity of the corresponding quotient Banach algebra. ....
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The study of finite semigroups is of interest because of its application inseveral branches of science, for instance, its uses and advantages in mathematics, computer science and finite machines are well-known. The power graph associated to such semigroups is also an ap More
The study of finite semigroups is of interest because of its application inseveral branches of science, for instance, its uses and advantages in mathematics, computer science and finite machines are well-known. The power graph associated to such semigroups is also an applicable tool in demonstrating the properties of semigroups. The completeness and Eulerianity of power graphs associated to finite commutative semigroups and finite non-commutative epigroups are studied in this paper. We show that these graphs may be non-complete for the monogenic semigroups and we gives a necessaryand sufficient condition for such graphs to be complete when finite regular epigroups are considered. This study answers in part the natural question”Is there any non-isomorphic non-group semigroups with the same complete power graph?”
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