alewife (gulf/**miscalled**) gulf menhaden brevoortia patronus. alewife (virginia) atlantic menhaden clupea harengus. all-mouth goosefish lophius americanus

374 T hai J. M ath. 9 (2011)/Y. Talebiand A. Mahmoudi inMifN+L=Mand Nisminimalwith respect to this property, orequivalenty, M=N+LandN∩L≪N. **Miscalled** an amply supplemented module if for any two submodulesA and Bof Mwith A+B=M, Bcontainsa supplement of A. **Miscalled** a supplemented module if ...

Apolynomialfof degree **miscalled** primitive ifk=2 m 1 is the smallest positive integer such that fdivides x k+1. A shift-register sequence with characteristic polynomial f (x) =x m + P m 1 i=0 c i x i is the sequence a= (a 0,a 1,...

A distribution Hon **Miscalled** integrable if for anyp 2 Mthereexistsa connectedsubmanifold L p ofMsuch thatT q L p =H q for all q 2L p. Such a submanifold L p is called an integral manifold of H.

For instance, a proper submodule P of **Miscalled** a prime submoduleif am 2 Pfora 2 R, and m 2 M, implies that m 2 Pora 2 (P: M). Prime submodules of modules were introduced by J. Dauns[9]and have been studied intensively since then (see for example, [2,5,7,14,16,17,18,22]).

A module **Miscalled** ef-extending if every closed submodule which contains essentiallya finitely generatedsubmodule is a direct summand of M. A ring Riscalled right ef-extending if R R is an ef-extending module.

Introduction to Factorization Theory Chapman Introduction and Motivation The Language of Non-Unique Factorizations Block Monoids Types of Monoids Examined in the Literature Numerical Monoids Some Notation Set A(M) =the set ofirreduciblesof M and P (M) =the set of prime elements of M: IfM=hA (M) i, then **Miscalled** atomic.

If an LP-Sasakianmanifold Mwiththecoecient satisfies the relation S (X,Y) =ag (X,Y) +b (X) (Y) , where a, bare the associated functions on the manifold, then the manifold **Miscalled** an-Einstein manifold.

A topological space **Miscalled** totally disconnected if each connected compo-nentofMconsists of one point. Exercise9.18. Show that Q, the space of rational numbers, in the topology induced by R, is totally disconnected, but not discrete.

AnR-module **Miscalled** torsion if for any m 2Mthere exists nonzeror 2 Rsuchthatrm=0. AnR-module **Miscalled** divisible if for any nonzeror 2 RwehaverM=M.