{"product_id":"sequentially-cohen-macaulay-and-regularity-of-monomial-ideals-von-sarfraz-ahmad","title":"Sequentially Cohen-Macaulay and Regularity of Monomial Ideals","description":"\u003cp\u003eIn the first chapter some basic notions and results  from commutative algebra are being introduced. In the second chapter we present new results  related  to sequentially Cohen Macaulay, pretty clean and Stanley ideals. Let I be  a monomial ideal of the poly- nomial ring S. We show that S=I is sequentially Cohen-Macaulay if and only if S=I is pretty clean.  In particular, if S=I is sequentially Cohen- Macaulay  then I is a Stanley ideal. Chapter 3 includes some results related to Stanley  Conjecture. We define nice partition of the multicomplex associated to a  Stanley ideal. In the main result we show that if the multicomplex associated to  monomial  ideal I has a nice partition then the multicomplex associated to polarized ideal  Ip has a nice partition. Fourth and last chapter deals with the regularity  of  ideals of Borel type. We have proved that the regularity of monomial ideals  whose associated prime ideals are totally ordered by inclusion is linearly bounded.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838339993\"\u003e\u003ch3\u003eStanley conjecture, Sequentially Cohen-Macaulay and Regularity of Monomial Ideals\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783838339993","offer_id":39499071848541,"sku":"9783838339993","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/88de1464-7a11-4787-94dc-d63e4e2dec10.jpg?v=1769841611","url":"https:\/\/shop.autorenwelt.de\/products\/sequentially-cohen-macaulay-and-regularity-of-monomial-ideals-von-sarfraz-ahmad","provider":"Autorenwelt Shop","version":"1.0","type":"link"}